Test Prep for AP® Courses

1.1Static Electricity and Charge: Conservation of Charge

1

When a glass rod is rubbed against silk, which of the following statements is true?

1. Electrons are removed from the silk.
2. Electrons are removed from the rod.
3. Protons are removed from the silk.
4. Protons are removed from the rod.
2

In an experiment, three microscopic latex spheres are sprayed into a chamber and become charged with +3e, +5e, and −3e, respectively. Later, all three spheres collide simultaneously and then separate. Which of the following are possible values for the final charges on the spheres? Select two answers.

X Y Z
(a) +4e −4e +5e
(b) −4e +4.5e +5.5e
(c) +5e −8e +7e
(d) +6e +6e −7e
Table 1.1
3

If objects X and Y attract each other, which of the following will be false?

1. X has positive charge and Y has negative charge.
2. X has negative charge and Y has positive charge.
3. X and Y both have positive charge.
4. X is neutral and Y has a charge.
4

Suppose a positively charged object A is brought in contact with an uncharged object B in a closed system. What type of charge will be left on object B?

1. Negative
2. Positive
3. Neutral
4. Cannot be determined
5

What will be the net charge on an object which attracts neutral pieces of paper but repels a negatively charged balloon?

1. Negative
2. Positive
3. Neutral
4. Cannot be determined
6

When two neutral objects are rubbed against each other, the first one gains a net charge of 3e. Which of the following statements is true?

1. The second object gains 3e and is negatively charged.
2. The second object loses 3e and is negatively charged.
3. The second object gains 3e and is positively charged.
4. The second object loses 3e and is positively charged.
7

In an experiment, a student runs a comb through his hair several times and brings it close to small pieces of paper. Which of the following will he observe?

1. Pieces of paper repel the comb.
2. Pieces of paper are attracted to the comb.
3. Some pieces of paper are attracted and some repel the comb.
4. There is no attraction or repulsion between the pieces of paper and the comb.
8

In an experiment a negatively charged balloon (balloon X) is repelled by another charged balloon Y. However, an object Z is attracted to balloon Y. Which of the following can be the charge on Z? Select two answers.

1. Negative
2. Positive
3. Neutral
4. Cannot be determined
9

Suppose an object has a charge of 1 C and gains 6.88 × 1018 electrons.

1. What will be the net charge of the object?
2. If the object has gained electrons from a neutral object, what will be the charge on the neutral object?
3. Find and explain the relationship between the total charges of the two objects before and after the transfer.
4. When a third object is brought in contact with the first object—after it gains the electrons—the resulting charge on the third object is 0.4 C. What was its initial charge?
10

The charges on two identical metal spheres (placed in a closed system) are -2.4 × 10−17 C and -4.8 × 10−17 C.

1. How many electrons will be equivalent to the charge on each sphere?
2. If the two spheres are brought in contact and then separated, find the charge on each sphere.
3. Calculate the number of electrons that would be equivalent to the resulting charge on each sphere.
11

In an experiment the following observations are made by a student for four charged objects W, X, Y, and Z:

• A glass rod rubbed with silk attracts W.

• W attracts Z but repels X.

• X attracts Z but repels Y.

• Y attracts W and Z.

Estimate whether the charges on each of the four objects are positive, negative, or neutral.

1.2Conductors and Insulators

12

Some students experimenting with an uncharged metal sphere want to give the sphere a net charge using a charged aluminum pie plate. Which of the following steps would give the sphere a net charge of the same sign as the pie plate?

1. Bringing the pie plate close to, but not touching, the metal sphere, then moving the pie plate away
2. Bringing the pie plate close to, but not touching, the metal sphere, then momentarily touching a grounding wire to the metal sphere
3. Bringing the pie plate close to, but not touching, the metal sphere, then momentarily touching a grounding wire to the pie plate
4. Touching the pie plate to the metal sphere
13
Figure 1.58 Balloon and sphere.

When the balloon is brought closer to the sphere, there will be a redistribution of charges. What is this phenomenon called?

1. Electrostatic repulsion
2. Conduction
3. Polarization
4. None of the above
14

What will be the charge at Y—the part of the sphere furthest from the balloon?

1. Positive
2. Negative
3. Zero
4. It can be positive or negative, depending on the material.
15

What will be the net charge on the sphere?

1. Positive
2. Negative
3. Zero
4. It can be positive or negative, depending on the material.
16

If Y is grounded while the balloon is still close to X, which of the following will be true?

1. Electrons will flow from the sphere to the ground.
2. Electrons will flow from the ground to the sphere.
3. Protons will flow from the sphere to the ground.
4. Protons will flow from the ground to the sphere.
17

If the balloon is moved away after grounding, what will be the net charge on the sphere?

1. Positive
2. Negative
3. Zero
4. It can be positive or negative, depending on the material.
18

A positively charged rod is used to charge a sphere by induction. Which of the following is true?

1. The sphere must be a conductor.
2. The sphere must be an insulator.
3. The sphere can be a conductor or insulator but must be connected to ground.
4. The sphere can be a conductor or insulator but must be already charged.
19
Figure 1.59 Rod and metal balls.

As shown in the figure above, two metal balls are suspended and a negatively charged rod is brought close to them.

1. If the two balls are in contact with each other what will be the charges on each ball?
2. Explain how the balls get these charges.
3. What will happen to the charge on the second ball—the ball further away from the rod—if it is momentarily grounded while the rod is still there?
4. If, instead of grounding, the second ball is moved away and then the rod is removed from the first ball, will the two balls have induced charges? If yes, what will be the charges? If no, why not?
20

Two experiments are performed using positively charged glass rods and neutral electroscopes. In the first experiment the rod is brought in contact with the electroscope. In the second experiment the rod is only brought close to the electroscope but not in contact. However, while the rod is close, the electroscope is momentarily grounded and then the rod is removed. In both experiments the needles of the electroscopes deflect, which indicates the presence of charges.

1. What is the charging method in each of the two experiments?
2. What is the net charge on the electroscope in the first experiment? Explain how the electroscope obtains that charge.
3. Is the net charge on the electroscope in the second experiment different from that of the first experiment? Explain why.

1.3Coulomb's Law

21

For questions 25–27, suppose that the electrostatics force between two charges is F.

What will be the force if the distance between them is halved?

1. 4F
2. 2F
3. F/4
4. F/2
22

Which of the following is false?

1. If the charge of one of the particles is doubled and that of the second is unchanged, the force will become 2F.
2. If the charge of one of the particles is doubled and that of the second is halved, the force will remain F.
3. If the charge of both the particles is doubled, the force will become 4F.
4. None of the above.
23

Which of the following is true about the gravitational force between the particles?

1. It will be 3.25 × 10−38F.
2. It will be 3.25 × 1038F.
3. It will be equal to F.
4. It is not possible to determine the gravitational force as the masses of the particles are not given.
24

Two massive, positively charged particles are initially held a fixed distance apart. When they are moved farther apart, the magnitude of their mutual gravitational force changes by a factor of n. Which of the following indicates the factor by which the magnitude of their mutual electrostatic force changes?

1. 1/n2
2. 1/n
3. n
4. n2
25
1. What is the electrostatic force between two charges of 1 C each, separated by a distance of 0.5 m?
2. How will this force change if the distance is increased to 1 m?
26
1. Find the ratio of the electrostatic force to the gravitational force between two electrons.
2. Will this ratio change if the two electrons are replaced by protons? If yes, find the new ratio.

1.4Electric Field: Concept of a Field Revisited

27

Two particles with charges +2q and +q are separated by a distance r. The +2q particle has an electric field E at distance r and exerts a force F on the +q particle. Use this information to answer questions 31–32.

What is the electric field of the +q particle at the same distance and what force does it exert on the +2q particle?

1. E/2, F/2
2. E, F/2
3. E/2, F
4. E, F
28

When the +q particle is replaced by a +3q particle, what will be the electric field and force from the +2q particle experienced by the +3q particle?

1. E/3, 3F
2. E, 3F
3. E/3, F
4. E, F
29

The direction of the electric field of a negative charge is ________.

1. Inward for both positive and negative charges
2. Outward for both positive and negative charges
3. Inward for other positive charges and outward for other negative charges
4. Outward for other positive charges and inward for other negative charges
30

The force responsible for holding an atom together is ________.

1. frictional
2. electric
3. gravitational
4. magnetic
31

When a positively charged particle exerts an inward force on another particle P, what will be the charge of P?

1. Positive
2. Negative
3. Neutral
4. Cannot be determined
32

Find the force exerted due to a particle having a charge of 3.2 × 10−19 C on another identical particle 5 cm away.

33

Suppose that the force exerted on an electron is 5.6 × 10−17 N, directed to the east.

1. Find the magnitude of the electric field that exerts the force.
2. What will be the direction of the electric field?
3. If the electron is replaced by a proton, what will be the magnitude of force exerted?
4. What will be the direction of force on the proton?

1.5Electric Field Lines: Multiple Charges

34

Consider two charges of unequal magnitude, $q1q1$ located at $x=−ax=−a$, and $q2q2$ located at $x=+ax=+a$ Calculate the electric field strength at a point on the positive y axis at $y=d.y=d.$ Then calculate the field at that point that would be produced by a single charge of magnitude $q1+q2q1+q2$ located at the origin. How does the distance affect the electric field? Is there a point at which the separation of charges becomes negligible?

35
Figure 1.60

An electric dipole—with +2q and –2q as the two charges—is shown in the figure above. A third charge, −q is placed equidistant from the dipole charges. What will be the direction of the net force on the third charge?

36
Figure 1.61

Four objects, each with charge +q, are held fixed on a square with sides of length d, as shown in the figure. Objects X and Z are at the midpoints of the sides of the square. The electrostatic force exerted by object W on object X is F. Use this information to answer questions 39–40.

What is the magnitude of force exerted by object W on Z?

1. F/7
2. F/5
3. F/3
4. F/2
37

What is the magnitude of the net force exerted on object X by objects W, Y, and Z?

1. F/4
2. F/2
3. 9F/4
4. 3F
38
Figure 1.62 Electric field with three charged objects.

The figure above represents the electric field in the vicinity of three small charged objects, R, S, and T. The objects have charges −q, +2q, and −q, respectively, and are located on the x-axis at −d, 0, and d. Field vectors of very large magnitude are omitted for clarity.

(a) i) Briefly describe the characteristics of the field diagram that indicate that the sign of the charges of objects R and T is negative and that the sign of the charge of object S is positive.

ii) Briefly describe the characteristics of the field diagram that indicate that the magnitudes of the charges of objects R and T are equal and that the magnitude of the charge of object S is about twice that of objects R and T.

For the following parts, an electric field directed to the right is defined to be positive.

(b) On the axes below, sketch a graph of the electric field E along the x-axis as a function of position x.

Figure 1.63 An Electric field (E) axis and Position (x) axis.

(c) Write an expression for the electric field E along the x-axis as a function of position x in the region between objects S and T in terms of q, d, and fundamental constants, as appropriate.

(d) Your classmate tells you there is a point between S and T where the electric field is zero. Determine whether this statement is true, and explain your reasoning using two of the representations from parts (a), (b), or (c).

1.6Conductors and Electric Fields in Static Equilibrium

39
Figure 1.64 A sphere conductor.

An electric field due to a positively charged spherical conductor is shown above. Where will the electric field be weakest?

1. Point A
2. Point B
3. Point C
4. same at all points
40
Figure 1.65 Electric field between two parallel metal plates.

The electric field created by two parallel metal plates is shown above. Where will the electric field be strongest?

1. Point A
2. Point B
3. Point C
4. Same at all points
41

Suppose that the electric field experienced due to a positively charged small spherical conductor at a certain distance is E. What will be the percentage change in electric field experienced at thrice the distance if the charge on the conductor is doubled?

42
Figure 1.66 Millikan oil drop experiment.

The classic Millikan oil drop experiment setup is shown above. In this experiment oil drops are suspended in a vertical electric field against the gravitational force to measure their charge. If the mass of a negatively charged drop suspended in an electric field of 1.18 × 10−4 N/C strength is 3.85 × 10−21 g, find the number of excess electrons in the drop.