Unit 7 Concepts Quiz

1. A proton and an electron are held apart a distance of 1 m and then released. As they approach each other, what happens to the force between them?

It gets bigger

It gets smaller

It stays the same

By Coulomb’s Law, the force between the two charges is inversely proportional to the distance squared. So, the closer they get to each other, the bigger the electric force between them gets!

Explanation

By Coulomb’s Law, the force between the two charges is inversely proportional to the distance squared. So, the closer they get to each other, the bigger the electric force between them gets!

2. Capacitor C1 is connected across a battery of 5 V. An identical capacitor C2 is connected across a battery of 10 V. Which one has the most charge?

C1

C2

Both have the same charge

It depends on other factors

Since Q = C V and the two capacitors are identical, the one that is connected to the greater voltage has the most charge, which is C2 in this case.

Explanation

Since Q = C V and the two capacitors are identical, the one that is connected to the greater voltage has the most charge, which is C2 in this case.

3. Two charged balls are repelling each other as they hang from the ceiling. What can you say about their charges?

One is positive, the other is negative

Both are positive

Both are negative

Both are positive or both are negative

The fact that the balls repel each other only can tell you that they have the same charge, but you do not know the sign. So they can be either both positive or both negative.

Explanation

The fact that the balls repel each other only can tell you that they have the same charge, but you do not know the sign. So they can be either both positive or both negative.

4. Consider point charges of +Q and +4Q, which are separated by 3.0 m. At what point, on a line between the two charges, would it be possible to place a charge of -Q such that the electrostatic force acting on it would be zero?

There is no such point possible.

1.0 m from the +Q charge

1.0 m from the +4Q charge

0.60 m from the +Q charge

According to Coulomb's Law, the electrostatic force between two charges is directly proportional to the product of the charges and inversely proportional to the square of the distance between them. Since the charges are of opposite signs, the electrostatic force will be attractive. In order for the electrostatic force on the -Q charge to be zero, the forces from the +Q and +4Q charges must cancel each other out. This can only occur if the -Q charge is placed at the midpoint between the two charges, which is 1.0 m from the +Q charge. At any other point, the forces will not balance out and the electrostatic force will not be zero.

Explanation

According to Coulomb's Law, the electrostatic force between two charges is directly proportional to the product of the charges and inversely proportional to the square of the distance between them. Since the charges are of opposite signs, the electrostatic force will be attractive. In order for the electrostatic force on the -Q charge to be zero, the forces from the +Q and +4Q charges must cancel each other out. This can only occur if the -Q charge is placed at the midpoint between the two charges, which is 1.0 m from the +Q charge. At any other point, the forces will not balance out and the electrostatic force will not be zero.

5. The force between two charges separated by a distance d is F. If the charges are pulled apart to a distance 3d, what is the force on each charge?

9F

3F

F

1/3F

1/9F

When the charges are pulled apart to a distance 3d, the force between them decreases. According to Coulomb's Law, the force between two charges is inversely proportional to the square of the distance between them. Therefore, if the distance is tripled, the force will decrease by a factor of 1/9. So, the force on each charge will be 1/9F.

Explanation

When the charges are pulled apart to a distance 3d, the force between them decreases. According to Coulomb's Law, the force between two charges is inversely proportional to the square of the distance between them. Therefore, if the distance is tripled, the force will decrease by a factor of 1/9. So, the force on each charge will be 1/9F.

6. A metal ball hangs from the ceiling by an insulating thread. The ball is attracted to a positive-charged rod held near the ball. The charge of the ball must be:

Positive

Negative

Neutral

Positive or neutral

Negative or neutral

Clearly, the ball will be attracted if its charge is negative. However, even if the ball is neutral, the charges in the ball can be separated by induction (polarization), leading to a net attraction.

Explanation

Clearly, the ball will be attracted if its charge is negative. However, even if the ball is neutral, the charges in the ball can be separated by induction (polarization), leading to a net attraction.

7. What must be done to a capacitor in order to increase the amount of charge it can hold (for a constant voltage)?

Increase the area of the plates

Decrease separation between the plates

Decrease the area of the plates

Either (1) or (2)

Either (2) or (3)

Since Q = C V, in order to increase the charge that a capacitor can hold at constant voltage, one has to increase its capacitance. Since the capacitance is given by C = eA/d, that can be done by either increasing A or decreasing d.

Explanation

Since Q = C V, in order to increase the charge that a capacitor can hold at constant voltage, one has to increase its capacitance. Since the capacitance is given by C = eA/d, that can be done by either increasing A or decreasing d.

8. You are sitting a certain distance from a point charge, and you measure an electric field of E₀. If the charge is doubled and your distance from the charge is also doubled, what is the electric field strength now?

4E

2E

E

1/2E

1/4E

Remember that the electric field is: E = kQ/r2. Doubling the charge puts a factor of 2 in the numerator, but doubling the distance puts a factor of 4 in the denominator, because it is distance squared!! Overall, that gives us a factor of 1/2.

Explanation

Remember that the electric field is: E = kQ/r2. Doubling the charge puts a factor of 2 in the numerator, but doubling the distance puts a factor of 4 in the denominator, because it is distance squared!! Overall, that gives us a factor of 1/2.

9. A parallel-plate capacitor initially has a potential difference of 400 V and is then disconnected from the charging battery. If the plate spacing is now doubled (without changing Q), what is the new value of the voltage?

100 V

200 V

400 V

800 V

1600 V

When the plate spacing is doubled without changing the charge (Q) on the capacitor, the capacitance (C) of the capacitor is halved. This is because the capacitance is inversely proportional to the plate spacing. Since the potential difference (V) across a capacitor is directly proportional to the charge and inversely proportional to the capacitance, when the capacitance is halved, the potential difference is doubled. Therefore, the new value of the voltage is 800 V.

Explanation

When the plate spacing is doubled without changing the charge (Q) on the capacitor, the capacitance (C) of the capacitor is halved. This is because the capacitance is inversely proportional to the plate spacing. Since the potential difference (V) across a capacitor is directly proportional to the charge and inversely proportional to the capacitance, when the capacitance is halved, the potential difference is doubled. Therefore, the new value of the voltage is 800 V.

10. A proton and an electron are in a constant electric field created by oppositely charged plates. You release the proton from the positive side and the electron from the negative side. Which feels the larger electric force?

Proton

Electron

Both feel the same force

Neither – there is no force

They feel the same magnitude force but opposite direction

Since F = qE and the proton and electron have the same charge in magnitude, they both experience the same force. However, the forces point in opposite directions because the proton and electron are oppositely charged.

Explanation

Since F = qE and the proton and electron have the same charge in magnitude, they both experience the same force. However, the forces point in opposite directions because the proton and electron are oppositely charged.