Q: A proton is released from rest at the positive plate of a parallel-plate capacitor with an electric field of $$50,000\ \mathrm{N/C}$$ and a plate separation of $$2.0\ \mathrm{mm}. $$What is the speed of the proton when it reaches the negative plate?

$$1.39 \times 10^5$\ \mathrm{m/s}$$

Q: A group of three charges are arranged as shown: $$2.0\ \mathrm{nC} at$$ $$(0,0)$$, $$3.0\ \mathrm{nC} at$$ $$(3.0\ \mathrm{cm}, 0)$$, and $$3.0\ \mathrm{nC} at$$ $$(0, 4.0\ \mathrm{cm}). $$What is the total electric potential energy of this system?

$$3.24 \times 10$$^{-6}$$\ \mathrm{J}$$

Q: A $$1\ \mathrm{mm}-$$diameter ball bearing has $$2 \times 10^9$ excess electrons. What is the electric potential of the ball bearing? (Assume the ball is isolated and spherical.)

$$-2.9 \times 10^4$\ \mathrm{V}$$

Q: A proton is accelerated from rest through a potential difference of $$1000\ \mathrm{V}. $$What is its final kinetic energy?

$$1.6 \times 10$$^{-16}$$\ \mathrm{J}$$

Question 1

Which of the following statements best describes why the electric force is considered a conservative force?

Accepted Answer

The work done by the electric force depends only on the initial and final positions, not the path taken.

Question 2

A proton is released from rest at the positive plate of a parallel-plate capacitor with an electric field of $$50,000\ \mathrm{N/C}$$ and a plate separation of $$2.0\ \mathrm{mm}. $$What is the speed of the proton when it reaches the negative plate?

Accepted Answer

$$1.39 	imes 10^5$\ \mathrm{m/s}$$

Question 3

What is the electric potential $$V at a $$distance $$r$$ from a point charge $$q$$?

Accepted Answer

$$V = k \dfrac{q}{r}$$

Question 4

Which of the following best describes an equipotential surface?

Accepted Answer

A surface where the electric potential is the same at every point.

Question 5

How much energy (in electron-volts) does an electron gain when it is accelerated through a potential difference of $$100\ \mathrm{V}$$?

Accepted Answer

$$100\ \mathrm{eV}$$

Question 6

A group of three charges are arranged as shown: $$2.0\ \mathrm{nC} at$$ $$(0,0)$$, $$3.0\ \mathrm{nC} at$$ $$(3.0\ \mathrm{cm}, 0)$$, and $$3.0\ \mathrm{nC} at$$ $$(0, 4.0\ \mathrm{cm}). $$What is the total electric potential energy of this system?

Accepted Answer

$$3.24 	imes 10$$^{-6}$$\ \mathrm{J}$$

Question 7

Which of the following is true about the relationship between electric field $$\vec{E}$$ and electric potential $$V$$?

Accepted Answer

$$\vec{E} = -
abla V$$

Question 8

A proton is fired with a speed of $$2.0 	imes 10^5$\ \mathrm{m/s}$$ from the midpoint of a parallel-plate capacitor towards the positive plate. The potential difference between the plates is $$500\ \mathrm{V}. $$Will the proton reach the positive plate?

Accepted Answer

No, because its initial kinetic energy is less than the potential energy barrier.

Question 9

What is the potential energy $$U of a $$system of two point charges $$q_1$$ and $$q_2$$ separated by a distance $$r$$?

Accepted Answer

$$U = k \dfrac{q_1$ q_2$}{r}$$

Question 10

A $$1\ \mathrm{mm}-$$diameter ball bearing has $$2 	imes 10^9$ excess electrons. What is the electric potential of the ball bearing? (Assume the ball is isolated and spherical.)

Accepted Answer

$$-2.9 	imes 10^4$\ \mathrm{V}$$

Question 11

Which of the following best explains why sparks can occur at a gas station when refueling a car?

Accepted Answer

The electric field near the nozzle exceeds the breakdown strength of air, causing ionization and a discharge.

Question 12

In the Millikan oil-drop experiment, what is the purpose of the electric field between the plates?

Accepted Answer

To balance the gravitational force on the charged oil droplets.

Question 13

If the electric field inside a conductor is zero, what can be said about the electric potential inside the conductor?

Accepted Answer

The electric potential is constant throughout the conductor.

Question 14

A proton is accelerated from rest through a potential difference of $$1000\ \mathrm{V}. $$What is its final kinetic energy?

Accepted Answer

$$1.6 	imes 10$$^{-16}$$\ \mathrm{J}$$

Question 15

Which of the following is true about the potential difference $$V_B - V_A$$ between two points in an electric field?

Accepted Answer

It depends only on the initial and final positions, not the path taken.

Question 16

Given the electric potential $$V(x, y, z)$$, how can you find the $$x-$$component of the electric field?

Accepted Answer

$$E_x = -\dfrac{\partial V}{\partial x}$$

Question 17

A proton is released from rest in a uniform electric field and moves a distance $$d in $$the direction of the field. What happens to its electric potential energy and kinetic energy?

Accepted Answer

Its electric potential energy decreases and its kinetic energy increases.

Question 18

What is the value of $$1\ \mathrm{eV} in $$joules?

Accepted Answer

$$1.60 	imes 10$$^{-19}$$\ \mathrm{J}$$

Question 19

Which of the following best describes the superposition principle for electric potential?

Accepted Answer

The total electric potential at a point is the sum of the potentials due to each individual charge.

Chapter 25: The Electric Potential – Physics with Calculus Study Notes

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