what would the force be if the separation between the two charges in the top window was adjusted to

Mastering Physics Solutions Chapter 19 Electric Charges, Forces, and Fields

Mastering Physics Solutions

Chapter 19 Electric Charges, Forces, and Fields Q.1CQ
When an object that was neutral becomes charged. does the full charge of the universechange? Explain
Solution:
No. charging of a neutral object does not change the full accuse of the universe If a neutral object is charged with another charged object the transfer of charge takes place between them
and then the net charge remains constant Hence, the total charge in the universe remains aforementioned

Chapter xix Electric Charges, Forces, and Fields Q.1P
CE PredictlExplain An electrically neutral object is given a positive charge. (a) In principle. does the object's mass increment, subtract, or stay the same as a result of existence charged? (b) Choose the best explanation from amongst the post-obit:
I To requite the object a positive charge we must remove some of its electrons: this will reduce its mass
ll Since electrical charges have mass, giving the object a positive accuse will increase its mass
llI Accuse is conserved, and therefore the mass of the object volition remain the sama
Solution:
(a) In club to requite the positive charge to any trunk we should remove the electrons from the body. And so some of the mass of the object volition Idecreased
(b) Every bit the removing of electrons leads to acquiring the positive charge this leads to decrease in mass of the object Hence best explanation is ( I).

Affiliate 19 Electrical Charges, Forces, and Fields Q.2CQ
The fact that the electron has a negative charge and the proton has a positive charge is due to a convention established past Benjamin Fran kIin Would there have been any pregnant consequences if Franklin had called the opposite convention? Is in that location any reward to naming charges plus and minus as opposed to. say. A and B?
Solution:
No.
When the current existing convention for the charge in the physics for electron & proton is interchange and so at that place would be no effect at all. because the net accuse in the universe will be same.
If the + & – charge are replaced by A & B. so in that location would be a problem for the defining of O (zero) accuse because O(aught) charge means, the object has equal number of positive & negative charge

Chapter 19 Electric Charges, Forces, and Fields Q.2P
CE PredictlExplain An electrically neutral object is given a negative accuse. (a) In principle. does the objects mass increment, subtract, or stay the same equally a effect of being charged? (b) Choose the best explanation from among the following:
I To give the object a negative charge we must give it more electrons, and this will increase its mass
II A positive charge increases an object's mass: a negative charge decreases its mass
IlI Charge is conserved, and therefore the mass of the object will remain the same
Solution:
(a)
An electrically neutral object acquires negative charge by addition of electrons These electrons will increase the mass of the object Hence, the total mass of the object will ¡n crease
(b)
Improver of more number of electrons results in acquiring negative charge by the object Therefore, the best explanation is

Affiliate 19 Electric Charges, Forces, and Fields Q.3CQ
Explicate why a comb that has been rubbed through your hair attracts pocket-size bits of paper. even though the paper is uncharged
Solution:
The plastic comb gets charged when information technology rubbed through our hair Here, the plastic comb gets negative charge and the hair gets positive charge. Like charges repel each other and the different charges attract each other.
When this negatively charged comb is placed near bits of newspaper then the electrons in each molecule of the bits of papers shill abroad from the combS As a result, the positive charge in the bit of paper comes close to the comb and charge separation takes place inside the bits of paper Hence, the chip of paper is polarized. Due to the electrostatic forcefulness between the negatively charged comb and the positive side of the paper they attracted by the rummage

Chapter 19 Electric Charges, Forces, and Fields Q.3P
CE (a) Based on the materials listed in Table 19—1, is the accuse of the rubber balloon shown on page 655 more probable to be positive or negative? Explain, (b) If the charge on the airship is reversed, will the stream, of water deflect toward or away from the airship? Explicate
Solution:
(a)
From the tabular array xix-1. 1 can infer that a rubber on rubbing acquires negative accuse and readily accepts more than number of electrons In the table specified, iv minus signs were given
for the cloth condom which means it is negatively charged. So. a airship made up of rubber will also possesses the same charge Thus, the safety balloon on rubbing acquires negative charge
(b)
H2o is a polar molecule that does not possess internet accuse. every bit i end of the water molecule possesses partial positive charge and the other finish possesses partial negative charge Assume that the charge on the balloon is reversed, that is. the charge on the balloon is positive If this positively charged balloon is brought near the stream of h2o, then the negative ends in the water molecule tend to align towards the positively charged balloon and positive ends in the water molecule movement towards the contrary cease As a result, the stream of water deflects towards the balloon In this case, the attractive
strength between the negatively charged particles of h2o and positively charged balloon is greater when compared to the repulsive strength between the positively charged particles of water and airship.
Thus, whatsoever exist the charge of the balloon, the water deflects towards the balloon considering of its polarity nature.

Affiliate 19 Electric Charges, Forces, and Fields Q.4CQ
Small bits of paper are attracted to an electrically charged comb, but every bit soon as they affect the comb they are strongly repelled Explicate this beliefs
Solution:
Bits of paper which are initially uncharged are attracted towards the electrically charged comb by polarization outcome, simply when they come in contact with the comb, the polarization result will disappear & paper receives the same accuse which shows the repulsion between them

Chapter nineteen Electric Charges, Forces, and Fields Q.4P
CE This problem refers to the information given in Table xix—1 (a) If rabbit fur is rubbed confronting glass. what is the sign of the charge each acquires? Explain. (b) Echo part (a) for the case of
drinking glass and rubber. (C) Comparing the situations described in parts (a) and (b). in which case is the magnitude of the tribo— electric accuse greater? Explain
Solution:
(a) Since the rabbit fur losses more than electrons while the glass gains the electrons, so, when rabbit fur is rubbed against glass, the fur attains positive charge and the glass rod acquires negative charge
(b) Since the safe has a tendency to proceeds the electrons so. when it rubbed confronting drinking glass. the glass acquires + ve charge and rubber — ve charge
(c) Rabbit fur and glass are side by side in the table where equally drinking glass and rubbers are widely separated So we can conclude that the magnitude of triboelectric charge is greater in the glass — rubber case than in rabbit fur — drinking glass case

Chapter 19 Electric Charges, Forces, and Fields Q.5CQ
A charged rod is brought near a suspended object. which is repelled by the rod Tin we conclude that the suspended object is charged? Explain
Solution:
Since the charged rod gets a repulsive force when it brought near a suspended object this observation clearly Indicates the object had the same Kind of charge on R Because the charges having lice signs are repel to each other

Chapter 19 Electric Charges, Forces, and Fields Q.5P
Find the net charge of a system consisting of 4.9 × 107 electrons.
Solution:

Affiliate 19 Electric Charges, Forces, and Fields Q.6CQ
A charged rod is brought most a suspended object. which is attracted to the rod Can nosotros conclude that the suspended object is charged? ExpIain
Solution:
May or may not have the charge
Since the charged rod gets an attractive forcefulness when it brought near a suspended object. this observation conspicuously indicates the object had either the opposite kind of charge or electrically neutral
Reason for get-go case: the charges having dissimilar signs are attracted to each other Reason for second instance: the charges attracts because of the polarization outcome

Affiliate xix Electric Charges, Forces, and Fields Q.6P
Discover the internet charge of a system consisting of (a) half dozen.15 × ten electrons and vii.44 × 106 protons or (b) 212 electrons and 165 protons.
Solution:

Chapter 19 Electric Charges, Forces, and Fields Q.7CQ
Describe some of the similarities and differences between Coulombs police force and Newton's law of gravity.
Solution:
The Coulomb forcefulness is proportional to the production of charges and the force is inversely proportional to the square of the distance between the ii charges. Hither, thousand is the coulomb'south constant. It is coulomb's law.
The gravitational force is proportional to the product of two different masses and inversely proportional to the square of the distance between the two masses. Here. 1000 is the gravitational constant. It is Newton'due south constabulary of gravitation.
Similarities between 's law of gravity and Coulomb'due south law:
1. Both the laws depend on the production of certain special properties of the objects.
Z Both the gravitational force and the electrostatic force are inversely proportional to the square of the distance between the objects
Dissimilarities:
one. In Newton'southward law of gravity, mass is relevant, and in Coulomb's police, the charge of the objects is irrelevant
2. Gravitational force is only bonny, whereas electrostatic strength tin be attractive or repulsive

Chapter 19 Electric Charges, Forces, and Fields Q.7P
How much negative electrical accuse is contained in 2 moles of carbon?
Solution:

Chapter 19 Electric Charges, Forces, and Fields Q.8CQ
A point charge +Q is fixed at a height H above the ground. Directly beneath this charge is a small ball with a charge −q and a mass m. When the brawl is at a height h above the ground, the net strength (gravitational plus electrical) interim on it is nada. Is this a stable equilibrium for the object? Explain.
Solution:

Affiliate 19 Electric Charges, Forces, and Fields Q.8P
Find the total electric accuse of 1.five kg of (a) electrons and (b) protons.
Solution:

Chapter 19 Electric Charges, Forces, and Fields Q.9CQ
Four identical point charges are placed at the corners of a foursquare. A 111th indicate charge placed at the center of the square experiences zip net force. Is this a stable equilibrium for the fifth accuse? Explicate.
Solution:
An object is said to be in mechanical equilibrium, if the object is in a state of rest or balance under the action of two or more external forces. This essentially means that at that place is no unbalanced force or cyberspace force and cyberspace torque interim on the object And hence there is no acceleration of the object Consider equal charges q is placed at the tour corners of a foursquare and consider the charge p exist placed at the centre of square Then, the charge p experiences two pairs of torces along the ii diagonals of the square and the torces by each pairs of charges are equal and contrary in management Thus, they abolish each other and experience no net torca This implies that the indicate charge in the eye is non accelerating Hence, the point charge in the center is said to be in stable equilibrium Therefore, the this is a example of stable equilibrium for the 5th charge every bit the outcome by all the charges on the fifth charge abolish

Chapter 19 Electrical Charges, Forces, and Fields Q.9P
A container holds a gas consisting of i.85 moles of oxygen molecules. One in a million of these molecules has lost a unmarried electron. What is the net charge of the gas?
Solution:

Chapter 19 Electric Charges, Forces, and Fields Q.10CQ
A proton moves in a region of abiding electric field. Does it follow that the proton'due south velocity is parallel to the electrical field? Does it follow that the proton'south dispatch is parallel to the electric field? Explain.
Solution:

Chapter xix Electrical Charges, Forces, and Fields Q.10P
The Charge on Agglutinative Tape When adhesive record is pulled from a dispenser, the discrete tape acquires a positive charge and the remaining tape in the dispenser acquires a negative charge. If the record pulled from the dispenser has 0.14 μC of charge per centimeter, what length of tape must exist pulled to transfer 1.8 × 1013 electrons to the remaining tape?
Solution:

Affiliate 19 Electric Charges, Forces, and Fields Q.11CQ
Draw some of the differences between charging by induction and charging by contact
Solution:
(i) Charging past induction does not involve whatsoever concrete contact betwixt the charging object and the object being charged Where as the charging past contact involves concrete contact to transfer accuse course one object to the other
(ii) When an object is charged by consecration, the object acquires a accuse opposite to that of the charging object. Charging past contact gives the object to exist charged the same charge as that of the charging object

Affiliate 19 Electrical Charges, Forces, and Fields Q.11P

Solution:

Chapter nineteen Electric Charges, Forces, and Fields Q.12CQ
A organisation consists of two charges of equal magnitude and reverse sign separated by a altitude d Since the total electrical accuse of this arrangement is zero, tin can we conclude that the electric field produced past the organisation is also zero? Does your reply depend on the separation if? Explain
Solution:
Consider two equal and opposite charges separated by a finite distance d The internet charge of the arrangement will be zero However information technology cannot be concluded that the net electric field produced by this system will be cypher. For example. consider a point which is closer to the positive charge. Now, the electric field at this point will be the vector sum of electric fields due to both positive and negative accuse Since the indicate is closer to positive charge than the negative accuse. magnitude of electric field due to positive charge will exist greater than magnitude of electric field due to negative accuse. Therefore. after the vector sum, the constructive electric field will be positive
However. if the separation becomes negligible (like the case when distance of point under consideration is much more than the separation distance d). the internet electrical field tin be said to be aught as both the charge will accept equal and opposite electrical fields at the point nether consideration

Chapter xix Electric Charges, Forces, and Fields Q.12P
A system of 1525 particles, each of wliich is either an electron or a proton, has a cyberspace accuse of −5.456 × 10−17 C. (a) How many electrons are in this organization?(b) What is the mass of this system?
Solution:

Affiliate nineteen Electric Charges, Forces, and Fields Q.13CQ
The forcefulness experienced by charge 1 at point A is different in direction and magnitude from the force experienced by charge ii at point B. Tin can nosotros conclude that the electric fields at points A and B are different? Explicate.
Solution:

Chapter 19 Electrical Charges, Forces, and Fields Q.13P
CE A charge +q and a charge −q are placed at contrary corners of a square. Will a third indicate accuse feel a greater force if it is placed at ane of the empty corners of the foursquare, or at the center of the square? Explain.
Solution:

Chapter nineteen Electric Charges, Forces, and Fields Q.14CQ
Can an electric tÏeId exist in a vacuum? Explain.
Solution:
Electromagnetic fields be in solids. liquids, gases. and the vacuum In the vacuum, the electromagnetic held propagates this has a component of electric & magnetic held
Yeah. the electric field exists in a vacuum.
Best instance is dominicus. The sun is a giant ball of nuclear reactions which creates not only light simply a large range of electromagnetic fields. Temper absorbs some of this energy and the spinning of the earth'due south gigantic cadre creates a huge magnetic field around the earthS This field points in the direction of one of the magnetic poles. At the poles of the globe, the magnetic field passes through the globe. Therefore, the field is smaller and causes the aurora borealis, the interaction of the sun'southward electromagnetic free energy with our atmosphere.

Chapter 19 Electric Charges, Forces, and Fields Q.14P
CE Repeat the previous question, this time with charges +q and +q at opposite corners of a foursquare.
Solution:

Chapter 19 Electric Charges, Forces, and Fields Q.15CQ
Explain why electric field lines never cross
Solution:
Electric field lines are imaginary lines to show the presence of the tield A tangent drawn at any indicate on the field line gives the direction of electric field at that point.
Consider ii lines intersect at a point then in such case two tangents can be drawn at that point which indicates ii directions of the electrical field Now if a unit charge is placed at that point then force acting on the unit charge due to field, is in 2 direction accordingly which is not possible. Since the electric force could non human activity in two directions at a position. Therefore. electric field lines tin never cross to each other

Chapter 19 Electric Charges, Forces, and Fields Q.15P

Solution:

Chapter 19 Electric Charges, Forces, and Fields Q.16CQ
Charge ql is within a airtight Gaussian surface: accuse q2 is but exterior the surface Does the electric flux through the surface depend on ql?Does information technology depend on q2?Explicate
Solution:
According to the Gauss Law, the electric flux through a surface depends on the charge that is enclosed by the surface And so the electric flux through the Gaussian surface depends on q1
Since the charge q2 is outside the Gaussian surface then. it has no effect on the total electric flux through the surface

Chapter 19 Electric Charges, Forces, and Fields Q.16P
CE Predict!Explicate Suppose the charged sphere in Active Example 19—2 is made from a conductor, rather than an insulator (a) Do yous expect the magnitude of the strength betwixt the
signal accuse and the conducting sphere to be greater than, less than, or equal to the strength between the indicate accuse and an insulating sphere? (b) Choose the best explanation from among the following:
I The conducting sphere will allow the charges to motility, resulting in a greater force.
Two The accuse of the sphere is the aforementioned whether information technology is conducting or insulating, and therefore the force is the same.
III The accuse on a conducting sphere will movement every bit far abroad equally possible from the indicate accuse. This results in a reduced forcefulness.
Solution:
(a)
The charge inside the conducting sphere comes on its surface. Hence, the resultant accuse value on sphere remains sama Therefore, the magnitude of electrostatic force between the conducting sphere and point accuse remains aforementioned as between an insulating sphere and signal charge
There is no change in the value of charge on conducting and insulating sphere. Hence, the magnitude of electrostatic force likewise remains unchanged
Hence, selection is the all-time explanation

Affiliate xix Electric Charges, Forces, and Fields Q.17CQ
In the previous question, does the electric field at a betoken on the Gaussian surface depend on q1?Does it depend on q2. Explicate.
Solution:

Affiliate 19 Electric Charges, Forces, and Fields Q.17P
At what separation is the electrostatic force betwixt a +11.2-μC point accuse and a +29.1-μCpoint charge equal in magnitude to i.57 N?
Solution:

Chapter 19 Electric Charges, Forces, and Fields Q.18CQ
Gauss's law can tell us how much charge ¡s contained inside a Gaussian surface Can information technology tell us where inside the surface it is located? Explain
Solution:
No.
The electrical flux through a surface depends on the full accuse enclosed by the surface but it is completely independent of location of the enclosed charges Hence Gauss police cannot tell us where within the surface the charge is located

Chapter 19 Electric Charges, Forces, and Fields Q.18P
The attractive electrostatic strength between the betoken charges +8.44 × 10−6 C and Q has a magnitude of 0.975 North when the separation between the charges is one.31 m. Find the sign and magnitude of the charge Q.
Solution:

Affiliate 19 Electrical Charges, Forces, and Fields Q.19CQ
Explain why Gauss'due south police force is non very useful in calculating the electric field of a charged disk.
Solution:

Affiliate 19 Electric Charges, Forces, and Fields Q.19P
If the speed of the electron in Case 19−ane were 73× 105 m/s, what would be the corresponding orbital radius?
Solution:

Chapter 19 Electric Charges, Forces, and Fields Q.20P
IP Ii bespeak charges, the first with a accuse of +3.13 × 10−6C and the second with a charge of −four.47 × ten−6 C, are separated by 25.5 cm. (a) Find the magnitude of the electrostatic force experienced past the positive accuse, (b) Is the magnitude of the force experienced past the negative charge greater than, less than, or the same as that experienced by the positive accuse? Explain.
Solution:

Affiliate 19 Electric Charges, Forces, and Fields Q.21P
When two identical ions are separated by a distance of 6.2 × 10−10 yard, the electrostatic force each exerts on the other is 5.4 × 10−9 N. How many electrons are missing from each ion?
Solution:

Chapter 19 Electric Charges, Forces, and Fields Q.22P
A sphere of radius iv.22 cm and uniform surface charge density +12.1 μC/m2 exerts an electrostatic force of magnitude 46.nine × ten−3 N on a bespeak accuse of +1.95 μC. Discover the separation between the point charge and the eye of the sphere.
Solution:

Affiliate 19 Electric Charges, Forces, and Fields Q.23P

Solution:

Affiliate 19 Electric Charges, Forces, and Fields Q.24P

Solution:

Chapter 19 Electric Charges, Forces, and Fields Q.25P

Solution:

Chapter 19 Electric Charges, Forces, and Fields Q.26P
IP Given that q = +12 μCand d = nineteen cm, (a) find the management and magnitude of the net electrostatic force exerted on the point accuse q2 in Figure nineteen−29. (b) How would your answers to part (a) change if the distance d were tripled?
Solution:

Chapter nineteen Electric Charges, Forces, and Fields Q.27P
Suppose the charge q2 in Effigy nineteen−29 tin be moved left or correct along the line connecting the charges q1 and q3. Given that q = +12 μC, find the altitude from q1 where q2 experiences a net electrostatic strength of zip. (The charges q1 and q3 are separated past a stock-still distance of 32 cm.)
Solution:

Chapter nineteen Electric Charges, Forces, and Fields Q.28P
Observe the orbital radius for which the kinetic energy of the electron in Case 19−i is one.51 eV. (Annotation: 1 eV = 1 electron volt = 1.6 × 10−19J.)
Solution:

Affiliate 19 Electrical Charges, Forces, and Fields Q.29P
Apoint charge q = −0.35 nC is fixed at the origin. Where must a proton be placed in society for the electric force acting on it to be exactly reverse to its weight? (Let the y axis be vertical and the x axis be horizontal.)
Solution:

Chapter 19 Electric Charges, Forces, and Fields Q.30P
A point accuse q = −0.35 nC is stock-still at the origin. Where must an electron exist placed in order for the electric force interim on it to be exactly contrary to its weight? (Let the y centrality be vertical and the x axis be horizontal.)
Solution:

Chapter 19 Electric Charges, Forces, and Fields Q.31P

Solution:

Chapter 19 Electric Charges, Forces, and Fields Q.32P
IP(a) Discover the direction and magnitude of the cyberspace electrostatic force exerted on the point charge q3 in Effigy 19−32. Let q = +two.4 μC and d = 27 cm. (b) How would your answers to part (a) change if the altitude d were doubled?
Solution:

Affiliate nineteen Electric Charges, Forces, and Fields Q.33P
IP Two point charges prevarication on the ten axis. A charge of +9.nine μC is at the origin, and a charge of −five.1 μC is at ten = x.0 cm. (a) At what position x would a third charge q3 be in equilibrium? (b) Does your answer to office (a) depend on whether q3 is positive or negative? Explain.
Solution:

Chapter xix Electrical Charges, Forces, and Fields Q.34P
A arrangement consists of two positive signal charges, q1 and q2> q1. The total charge of the system is +62.0 μC, and each accuse experiences an electrostatic force of magnitude 85.0 Due north when the separation between them is 0.270 m. Find q1 and q2
Solution:

Affiliate 19 Electrical Charges, Forces, and Fields Q.35P

Solution:

Chapter 19 Electric Charges, Forces, and Fields Q.36P
Referring to Problem 35, suppose that the magnitude of the internet electrostatic forcefulness exerted on the point accuse q2 in Effigy 19−33 is 0.65 N. (a) Find the distance d. (b) What is the direction of the internet force exerted on q2?
Solution:

Affiliate 19 Electric Charges, Forces, and Fields Q.37P
IP (a) If the nucleus in Example xix−1 had a accuse of +2e (every bit would be the case for a nucleus of helium), would the speed of the electron be greater than, less than, or the same as that plant in the Example? Explicate. (Presume the radius of the electron's orbit is the same.) (b) Discover the speed of the electron for a nucleus of charge +2e.
Solution:

Chapter 19 Electric Charges, Forces, and Fields Q.38P
Iv point charges are located at the corners of a square with sides of length a. Two of the charges are +q, and ii are −q, Observe the magnitude and direction of the net electrical strength exerted on a accuse +Q, located at the center of the square, for each of the following two arrangements of charge: (a) The charges alternate in sign (+q, −q, +q, −q) as you go around the square; (b) the two positive charges are on the peak corners, and the two negative charges are on the lesser corners.
Solution:

Affiliate 19 Electric Charges, Forces, and Fields Q.39P
IP Two identical point charges in free space are connected by a string seven.vi cm long. The tension in the string is 0.21 North. (a) Find the magnitude of the charge on each of the point charges, (b) Using the information given in the trouble statement, is information technology possible to decide the sign of the charges? Explain, (c) Detect the tension in the string if +1.0 μC of charge is transferred from 1 indicate charge to the other. Compare with your issue from part (a).
Solution:

Chapter 19 Electric Charges, Forces, and Fields Q.40P
Two spheres with uniform surface charge density, one with a radius of 7.ii cm and the other with a radius of 4.seven cm, are separated by a centre−to−center altitude of 33 cm. The spheres accept a combined charge of +55 μCand repel one some other with a force of 0.75 North. What is the surface charge density on each sphere?
Solution:

Chapter xix Electric Charges, Forces, and Fields Q.41P
Point charges, q1 and q2, are placed on the x centrality, with q1 at x = 0 and q2 at x = d. Athird signal charge, +Q, is placed at x = 3d/4. if the net electrostatic force experienced by the charge +Q is zero, how are q1 and q2 related?
Solution:

Chapter 19 Electrical Charges, Forces, and Fields Q.42P
CE Two electric charges are separated by a finite distance. Somewhere betwixt the charges, on the line connecting them, the net electric field they produce is zero, (a) Exercise the charges have the same or opposite signs? Explicate, (b) If the point of zip field is closer to charge 1, is the magnitude of accuse 1 greater than or less than the magnitude of charge ii? Explain.
Solution:

Chapter 19 Electrical Charges, Forces, and Fields Q.43P
What is the magnitude of the el ectric field produced by a charge of magnitude seven.50 μCat a distance of (a) one.00 chiliad and (b) ii.00 m?
Solution:

Chapter 19 Electric Charges, Forces, and Fields Q.44P
A +5.0 μC charge experiences a 0.44−North force in the positive y direction. If this charge is replaced with a − ii.7μCcharge, what forcefulness will it experience?
Solution:

Chapter 19 Electric Charges, Forces, and Fields Q.45P
Two point charges he on the x axis. A charge of +6.2 μC is at the origin, and a charge of −9.5 μCis at 10 = 10.0 cm. What is the net electric field at (a) x = −four.0 cm and at (b) ten = +iv.0 cm?
Solution:

Chapter xix Electric Charges, Forces, and Fields Q.46P
CE The electric field on the dashed Une in Effigy nineteen−28 vanishes at infinity, but also at two different points a finite altitude from the charges. Identify the regions in which you can notice Eastward = 0 at a finite distance from the charges: region 1, to the left of point A; region ii, between points A and B; region iii, between points B and C; region 4, to the right of point C.
Solution:

Chapter 19 Electric Charges, Forces, and Fields Q.47P
An object with a accuse of −3.half-dozen μC and a mass of 0.012 kg experiences an upward electric force, due to a uniform electric field, equal in magnitude to its weight, (a) Notice the direction and magnitude of the electric field, (b) If the electric charge on the object is doubled while its mass remains the same, observe the direction and magnitude of its dispatch.
Solution:

Chapter 19 Electrical Charges, Forces, and Fields Q.48P
IP Figure nineteen−33 shows a system consisting of three charges, q1 = +v.00 μC, q2 = +v.00 μC, and q3 = −v.00 μC, at the vertices of an equilateral triangle of side d = 2.95 cm. (a) Detect the magnitude of the electric field at a signal halfway between the charges q1 and q2. (b) Is the magnitude of the electric field halfway between the charges q2 and q3 greater than, less than, or the same as the electric field found in part (a)? Explain, (c) Detect the magnitude of the electric field at the point specified in office (b).
Solution:

Chapter nineteen Electric Charges, Forces, and Fields Q.49P
Two point charges of equal magnitude are 7.5 cm apart. At the midpoint of the line connecting them, their combined electric field has a magnitude of 45 N/C. Discover the magnitude of the charges.
Solution:

Affiliate 19 Electric Charges, Forces, and Fields Q.50P
IP A point accuse q1 = +4.seven μCis placed at each corner of an equilateral triangle with sides 0.21 thou in length, (a) What is the magnitude of the electric field at the midpoint of any of the iii sides of the triangle? (b) Is the magnitude of the electric field at the center of the triangle greater than, less than, or the same as the magnitude at the midpoint of a side? Explain.
Solution:

Affiliate 19 Electrical Charges, Forces, and Fields Q.51P
IP Iv bespeak charges, each of magnitude q, are located at the corners of a square wi th sides of length a. Two of the charges are +q, and two aie −q. The charges are bundled in one of the following 2 means: (1) The charges alternate in sign (+q, −q, +q, −q) as you go around the square; (2) the top 2 comers of the square have positive charges (+q, +q), and the bottom two corners have negative charges (−q, −q). (a) In which instance will the electric field at the center of the square take the greatest magnitude? Explain, (b) Calculate the electric field at the center of the square for each of these ii cases.
Solution:

.

Affiliate 19 Electric Charges, Forces, and Fields Q.52P
The electric field at the point 10 = 5.00 cm and y = 0 points in the positive ten direction with a magnitude of ten.0 N/C. At the point x = 10.0 cm and y = 0 the electric field points in the positive x direction with a magnitude of 15.0 Northward/C. Bold this electric field is produced by a single signal accuse, find (a) its location and (b) the sign and magnitude of its accuse.
Solution:

Affiliate 19 Electrical Charges, Forces, and Fields Q.53P

Solution:

Chapter nineteen Electric Charges, Forces, and Fields Q.54P
Make a qualitative sketch of the electrical field lines produced by ii equal positive charges, +q, separated past a distance d.
Solution:

Affiliate 19 Electrical Charges, Forces, and Fields Q.55P
Make a qualitative sketch of the electric field lines produced past two charges, +q and −q, separated by a distance d.
Solution:

Affiliate nineteen Electric Charges, Forces, and Fields Q.56P
Referring to Figure 19-34, suppose q2 is not known. Instead, it is given that q1 + q2 = −two.5 μC. Find q1 q2, and q3.
Solution:

Affiliate 19 Electric Charges, Forces, and Fields Q.57P
Brand a qualitative sketch of the electric field lines produced by the four charges, +q, −q, +q, and −q, bundled clockwise on the four corners of a square with sides of length d.
Solution:

Chapter 19 Electric Charges, Forces, and Fields Q.58P
Sketch the electric field lines for the system of charges shown in Figure nineteen-29.
Solution:

Chapter 19 Electric Charges, Forces, and Fields Q.59P
Sketch the electric field lines for the system of charges described in Trouble 35.
Solution:

Affiliate 19 Electric Charges, Forces, and Fields Q.60P
Suppose the magnitude of the electric field between the plates in Example nineteen-vi is changed, and a new object with a charge of −2.05 μC is attached to the string. If the tension in the string is 0.450 Due north, and the angle it makes with the vertical is 16°, what are (a) the mass of the object and (b) the magnitude of the electric field?
Solution:

Chapter 19 Electric Charges, Forces, and Fields Q.61P
CE Predict/Explain Gaussian surface 1 has twice the surface area of Gaussian surface two. Both surfaces enclose the aforementioned charge Q. (a) Ts the electric flux through surface 1 greater than, less than, or the same equally the electrical flux through surface ii? (b) Choose the best explanation from among the post-obit:
I. Gaussian surface ii is closer to the charge, since information technology has the smaller area. It follows that it has the greater electric flux.
Ii. The two surfaces enclose the same accuse, and hence they have the same electrical flux.
III. Electric flux is proportional to area. Every bit a outcome, Gaussian surface ane has the greater electric flux.
Solution:

Chapter 19 Electric Charges, Forces, and Fields Q.62P
CESuppose the conducting shell in Figure 19-25−which has a point charge +Q at its center−has a nonzero net accuse. How much charge is on the inner and outer surface of the crush when the net charge of the shell is (a) −2Q, (b) −Q, and (c) +Q?
Solution:

Chapter nineteen Electrical Charges, Forces, and Fields Q.63P

Solution:

Chapter 19 Electric Charges, Forces, and Fields Q.64P
A compatible electric field of magnitude 25,000 N/C makes an angle of 37° with a plane surface of expanse 0.0153 m2, What is the electric flux through this surface?
Solution:

Affiliate nineteen Electric Charges, Forces, and Fields Q.65P
A surface encloses the charges q1 = iii.2 μC, q2 − six.ix μC, and q3 = −4.1 μC. Find the electric flux through this surface.
Solution:

Affiliate nineteen Electrical Charges, Forces, and Fields Q.66P
IPA uniform electric field of magnitude 6.00 × 103 N/C points upwards. An empty, closed shoe box has a superlative and bottom that are 35.0 cm past 25.0 cm, vertical ends that are 25.0 cm by 20.0 cm, and vertical sides tha t are 20.0 cm by 35.0 cm. (a) Which side of the box has the greatest positive electric flux? Which side has the greatest negative electric flux? Which sides take zero electric flux? (b) Calculate the electric flux through each of the six sides of the box.
Solution:

Affiliate xix Electric Charges, Forces, and Fields Q.67P
BIO Nerve Cells Nerve cells are long, thin cylinders along which electrical disturbances (nervus impulses) travel. The cell membrane of a typical nerve prison cell consists of an inner and an outer wall separated by a distance of 0.10 μ thou. The electric field within the cell membrane is 7.0 × 105 N/C. Approximating the cell membrane as a parallel-plate capacitor, determine the magnitude of the accuse density on the inner and outer prison cell walls.
Solution:

Chapter 19 Electric Charges, Forces, and Fields Q.68P

Solution:

Affiliate nineteen Electric Charges, Forces, and Fields Q.69P
Consider a spherical Gaussian surface and 3 charges: q1 = i.61 μC,q2 = −2.62 μC, and q3 = 3.91 μC. Find the electric flux through the Gaussian surface if it completely encloses (a) only charges q1 and q2, (b) only charges q2 and q3, and (c) all 3 charges, (d) Suppose a quaternary charge, Q, is added to the situation described in function (c). Find the sign and magnitude of Q required to give zero electric flux through the surface.
Solution:

Affiliate xix Electric Charges, Forces, and Fields Q.70P

Solution:

Chapter 19 Electric Charges, Forces, and Fields Q.71GP
CE Predict/Explain An electron and a proton are released from rest in space, far from any other objects. The particles motion toward each other, due to their mutual electrical attraction. (a) When they meet, is the kinetic energy of the electron greater than, less than, or equal to the kinetic energy of the proton? (b) Choose the best explanation from among the following:
I. The proton has the greater mass. Since kinetic energy is proportional to mass, it follows that the proton will have the greater kinetic energy.
II. The two particles experience the same force, simply the light electron moves farther than the massive proton. Therefore, the work done on the electron, and hence its kinetic energy, is greater.
III. The aforementioned forcefulness acts on the two particles. Therefore, they will have the same kinetic energy and energy will be conserved.
Solution:

Affiliate 19 Electric Charges, Forces, and Fields Q.72GP
CE Predict/Explain In Conceptual Checkpoint 19−3, suppose the charge to be placed at cither betoken A or point B is +q rather than − q, (a) Is the magnitude of the cyberspace force experienced by the movable charge at point A greater than, less than, or equal to the magnitude of the cyberspace forcefulness at point B? (b) Cull the best explanation from among the following:
I. Point B is farther from the two fixed charges. Equally a result, the cyberspace strength at point B is less than at point A. Ii. The net strength at point A cancels, just equally information technology does in Conceptual Checkpoint 19−3. Therefore, the nonzero net force at bespeak B is greater in magnitude than the zero net force at betoken A.
III. The internet force is greater in magnitude at point A because at that location the movable charge experiences a net repulsion from each of the fixed charges.
Solution:

Chapter 19 Electric Charges, Forces, and Fields Q.73GP
CE An electron (charge = −e) orbits a helium nucleus (charge = +2e). Is the magnitude of the strength exerted on the he− Hum nucleus by the electron greater than, less than, or the same as the magnitude of the forcefulness exerted on the electron past the helium nucleus? Explicate.
Solution:

Chapter nineteen Electric Charges, Forces, and Fields Q.74GP
CE In the operating room, technicians and doctors must have care non to create an electric spark, since the presence of the oxygen gas used during an functioning increases the hazard of a deadly fire. Should the operating−room personnel wear shoes that are conducting or not-conducting? Explicate.
Solution:
The operating room personnel should habiliment shoes that are conducting and so that any charge they transform while walking, can flow into the basis.

Chapter 19 Electrical Charges, Forces, and Fields Q.75GP
CE Under normal atmospheric condition, the electric field at the surface of the Earth points down, into the ground. What is the sign of the electrical charge on the ground?
Solution:
We know that electric field lines indicate in the direction of negative charges.So the accuse on Earth must be negative

Chapter 19 Electric Charges, Forces, and Fields Q.76GP
CE Two identical spheres are fabricated of conducting material. Initially, sphere i has a net charge of +35Q and sphere 2 has a net charge of −26Q. If the spheres are now brought into contact, what is the final charge on sphere 1? Explain.
Solution:

Affiliate 19 Electric Charges, Forces, and Fields Q.77GP
CE A Gaussian surface for the charges shown in Figure 19−35 has an electrical flux equal to +3q/ε0. Which charges arc contained within this Gaussian surface?
Solution:

Chapter nineteen Electric Charges, Forces, and Fields Q.78GP
A proton is released from balance in a compatible electric field of magnitude 1.08 × 105 Due north/C. Observe the speed of the proton after information technology has traveled (a) ane.00 cm and (b) ten.0 cm.
Solution:

Chapter 19 Electric Charges, Forces, and Fields Q.79GP
BIO Ventricular Fibrillation If a charge of 0.30 C passes through a person'southward chest in ane.0 s, the heart can go into ventricular fibrillation−a nonrhythmic "fluttering" of the ventricles that results in fiddling or no claret beingness pumped to the trunk. If this rate of charge transfer persists for 4.5 s, how many electrons pass through the chest?
Solution:

Affiliate 19 Electric Charges, Forces, and Fields Q.80GP

Solution:

Chapter xix Electric Charges, Forces, and Fields Q.81GP

Solution:

Chapter 19 Electric Charges, Forces, and Fields Q.82GP
Find (a) the management and (b) the magnitude of the net electric field at the center of the equilateral triangle in Figure 19−31. Give your answers in terms of the angle θ, as divers in Figure 19−31, and E, the magnitude of the electric field produced by whatsoever oneof the charges at the middle of the triangle.
Solution:

Affiliate 19 Electrical Charges, Forces, and Fields Q.83GP
At the moment, the number of electrons in your body is essentially the same as the number of protons, giving you a net charge of zero. Suppose, notwithstanding, that this balance of charges is off by 1% in both yous and your friend, who is 1 meter away. Estimate the magnitude of the electrostatic forcefulness each of yous experiences, and compare it with your weight.
Solution:

Chapter 19 Electric Charges, Forces, and Fields Q.84GP
A small-scale object of mass 0.0150 kg and accuse 3.1 μChangs from the ceiling by a thread. A second small object, with a charge of 4.two μC, is placed i.2 1000 vertically below the kickoff accuse. Find (a) the electric field at the position of the upper charge due to the lower accuse and (b) the tension in the thread.
Solution:

Affiliate xix Electric Charges, Forces, and Fields Q.85GP
IP Consider a organization of three point charges on the x axis. Charge i is at x = 0, charge 2 is at x = 0.xx g, and charge 3 is at 10 = 0.40 chiliad. In addition, the charges have the following values: q1 = −19 μC, q2 = q3 = +nineteen μC(a)The electrical field vanishes at some point on the ten axis between 10 = 0.20 yard and x = 0.xl m. Ts the betoken of aught field (i) at x = 0.xxx m, (ii) to the left of x = 0.30 m, or (3) to the right of x = 0.30 yard? Explain, (b) observe the point where E = 0 between ten = 0.20 m and x = 0.40 one thousand.
Solution:

Chapter xix Electric Charges, Forces, and Fields Q.86GP
IP Consider the system of 3 point charges described in the previous problem, (a) The electric field vanishes at two different points on the.x centrality. One betoken is between ten = 0.20 thou and x = 0.twoscore m. Is the 2nd betoken located to the left of charge i or to the correct of charge three? Explain, (b) Find the value of x at the second point where East = 0.
Solution:

Affiliate 19 Electric Charges, Forces, and Fields Q.87GP
The electric field at a radial distance of 47.7 cm from the thin charged wire shown in Figure 19−36 has a magnitude of 35,400 Northward/C. (a) Using the outcome given in Trouble 70, what is the magnitude of. the charge per length on this wire? (b) At what altitude from the wire is the magnitude of the electric field equal to ?
Solution:

Chapter xix Electric Charges, Forces, and Fields Q.88GP
A organization consisting entirely of electrons and protons has a net charge of 1.84 × 10−fifteen C and a internet mass of iv.56 × 10−23 kg. How many (a) electrons and (b) protons are in this system?
Solution:

Chapter 19 Electric Charges, Forces, and Fields Q.89GP

Solution:

Affiliate xix Electric Charges, Forces, and Fields Q.90GP
IP Consider the system of three charges described in the previous problem and shown in Effigy 19−38. (a) Practise you wait the net strength acting on charge 1 to have a magnitude greater than, less than, or the same as the magnitude of the internet forcefulness acting on charge 2? Explicate, (b) Find the magnitude of the net force acting on charge 1. (c) Find the magnitude of the internet force acting on accuse 2.
Solution:

Chapter 19 Electrical Charges, Forces, and Fields Q.91GP
IP BIO Prison cell Membranes The cell membrane in a nerve cell has a thictcness of 0.12μ k. (a) Approximating the cell membrane every bit a parallel−plate capacitor with a surface charge density of five.9 × 10−6 C/m2, find the electric field within the membrane, (b) If the thickness of the membrane were doubled, would your respond to part (a) increment, decrease, or stay the same? Explain.
Solution:

Affiliate 19 Electric Charges, Forces, and Fields Q.92GP
A foursquare with sides of length L has a indicate charge at each of its four corners. Two corners that are diagonally reverse accept charges equal to +two.25 μC; the other 2 diagonal comers take charges Q. Discover the magnitude and sign of the charges Q such that each of the +two.25μC charges experiences zero internet forcefulness.
Solution:

Chapter 19 Electric Charges, Forces, and Fields Q.93GP
IP Suppose a charge +Q is placed on the Earth, and another charge +Q is placed on the Moon. (a) Observe the value of Q needed to "residual" the gravitational attraction betwixt the Earth and the Moon. (b) How would your respond to part (a) change if the distance between the Earth and the Moon were doubled? Explain.
Solution:

Affiliate nineteen Electric Charges, Forces, and Fields Q.94GP

Solution:

Chapter 19 Electric Charges, Forces, and Fields Q.95GP
A modest sphere with a charge of +2.44 μCis attached to a relaxed horizontal leap whose force constant is 89.two N/m. The spring extends along the ten centrality, and the sphere rests on a frictionless surface with its center at the origin. A signal charge Q = −viii.55 μCis now moved slowly from infinity to a bespeak x = d > 0 on the 10 axis. This causes the pocket-size sphere to motility to the position x = 0.124 one thousand. Detect d.
Solution:

Chapter xix Electrical Charges, Forces, and Fields Q.96GP
Twelve identical betoken charges q are equally spaced around the circumference of a circle of radius R. The circumvolve is centered al the origin. One of the twelve charges, which happens to be on the positive 10 axis, is at present moved to the center of the circle. Observe (a) the management and (b) the magnitude of the internet electric strength exerted on this charge.
Solution:

Affiliate 19 Electric Charges, Forces, and Fields Q.97GP
BIO Nerve Impulses When a nerve impulse propagates along a nervus cell, the electrical field within the prison cell membrane changes from 7.0 × 105 Due north/C inone direction to three.0 × 105 N/C in the other direction. Approximating the prison cell membrane as a parallel−plate capacitor, notice the magnitude of the change in charge density on the walls of the cell membrane.
Solution:

Chapter xix Electric Charges, Forces, and Fields Q.98GP
IP The Electric Field of the Earth The Earth produces an approximately uniform electric field at ground level. This electric field has a magnitude of 110 N/C and points radially inward, toward the center of the World. (a) Find the surface charge density (sign and magnitude) on the surface of the Earth. (b) Given that the radius of the World is vi.38 × 106 m, find the total electric accuse on the Earth. (c) If the Moon had the aforementioned amount of electric charge distributed uniformly over its surface, would its electric field at the surface exist greater than, less than, or equal to 110 N/C? Explain.
Solution:

Affiliate 19 Electric Charges, Forces, and Fields Q.99GP

Solution:

Chapter xix Electrical Charges, Forces, and Fields Q.100GP
Four identical charges, +Q, occupy the corners of a square with sides of length a. A fifth charge, q, can exist placed at any desired location. Find the location of the 5th charge, and the value of q, such that the net electric force acting on each of the original 4 charges, +Q, is nix.
Solution:

Chapter xix Electric Charges, Forces, and Fields Q.101GP

Solution:

Chapter nineteen Electrical Charges, Forces, and Fields Q.102GP
Two identical conducting spheres are separated by a stock-still center−to−center altitude of 45 cm and take different charges. Initially, the spheres attract each other with a force of 0.095 N. The spheres are now connected by a thin conducting wire. Afterward the wire is removed, the spheres are positively charged and repel 1 another with a force of 0.032 N. Find (a) the final and (b) the initial charges on the spheres.
Solution:

Chapter xix Electric Charges, Forces, and Fields Q.103PP
How many electrons must be transferredaway from a bee to produce a charge of +93.0 pC?
A. 1.72 × 10−ix
B. five.81 × 108
C. ane.02 × 1020
D. one.49 × 1029
Solution:

Chapter nineteen Electric Charges, Forces, and Fields Q.104PP
Suppose ii bees, each with a charge of 93.0 pC, are separated by a distance of i.20 cm. Treatingthe bees as betoken charges, what is the magnitude of the electrostatic force experienced past the bees? (In comparison, the weight of a 0.140g bee is 1.37 × x−3 Northward.)
A. 6.01 × 10−17 Northward
B. 6.48 × 10−9 N
C. 5.40 × 10−7N
D. 5.81 × 10−3N
Solution:

Chapter 19 Electric Charges, Forces, and Fields Q.105PP
The force required to disassemble a grain of pollen from an avocado stigma is approximately 4.0 × 10−five Northward. What is the maximum distance at which the electrostatic strength betwixt a bee and a grain of pollen is sufficient to detach the pollen? Treat the bee and pollen as point charges, and assume the pollen has a accuse opposite in sign and equal in magnitude to the bee.
A. iv.7 × ten−7 m
B. i.nine mm
C. 4.4 cm
D. 220 m
Solution:

Affiliate 19 Electric Charges, Forces, and Fields Q.106PP
The Earth produces an electric field of magnitude 110 N/C. What strength does this electric field exert on a bee carrying a accuse of 93.0 pC? (Again, for comparison, the weight of a bee is approximately 1.37 × 10−three Due north.)
A. 1.76 × 10−17N
B. S.45 × 10−thirteen N
C. 1.02 × 10−8 N
D. i.13 × 10−six Northward
Solution:

Chapter 19 Electric Charges, Forces, and Fields Q.107IP
IP Referring to Instance 19−five Suppose q1 = +2.90μC is no longer at the origin, merely is now on the y axis betwixt y = 0 and y = 0.500 k. Thecharge q2 = +2.90 μCis at ten = 0 and y = 0.500 g, and betoken 3 is at 10 = y = 0.500 thou. (a) Is the magnitude of the net electric field at point 3, which we call Enct, greater than, less than, or equal to its previous value? Explicate. (b) Is the bending θ that Enct makes with the x axis greater than, less than, or equal to its previous value? Explain. Find the new values of (c) Enct and (d) θ if q1 is at y = 0.250 m.
Solution:

Affiliate nineteen Electric Charges, Forces, and Fields Q.108IP
IP Referring to Example 19−5 In this arrangement, the charge q1 is at the origin, the charge q2 is at x = 0 and y = 0.500 m, and point iii is at 10 = y = 0.500 one thousand. Suppose that q1 = + 2.90 μC, only that q2 isincreased to a value greater than +2.90 μC. As a result, do (a) Enct and (b) θ increase, decrease, or stay the same? Explain. If Enct = i.66 × 105 North/C, observe (c) q2 and (d) θ.
Solution:

Chapter 19 Electrical Charges, Forces, and Fields Q.109IP
IP Referring to Example 19−6 The magnitude of the charge is changed until the angle the thread makes with the vertical is θ = xv.0°. The electrical field is i.46 × 104 Due north/C and the mass of the object is 0.0250 kg. (a) Is the new magnitude of q greater than or less than its previous value? Explicate. (b) Find the new value of q.
Solution:

Affiliate xix Electrical Charges, Forces, and Fields Q.110IP
Referring to Case 19−6 Suppose the magnitude of the electric field is adjusted to give a tension of 0.253 N in the thread. This will also change the angle the thread makes with the vertical. (a) Detect the new value of E. (b) Find the new angle between the thread and the vertical.
Solution:

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