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AP Physics C: Electricity and Magnetism Practice Quiz: Electric Potential Energy

Written by AP Content Team, Verified for 2026 AP Exams, Last updated: May 2026

Test your understanding with short quizzes. This quiz has 9 questions to check your progress.

Question 1 of 9

Which of the following equations correctly represents the general form for the electric potential energy between two charged objects, q1 and q2, separated by a distance r?

All Questions (9)

Which of the following equations correctly represents the general form for the electric potential energy between two charged objects, q1 and q2, separated by a distance r?

A) U_E = k * (q1*q2) / r^2

B) U_E = k * (q1+q2) / r

C) U_E = k * (q1*q2) / r

D) U_E = k * q1 / r

Correct Answer: C

The provided content explicitly gives the equation for the electric potential energy between two charged objects as U_E = k * (q1*q2) / r.

A system consists of two objects with positive charges. If the distance 'r' between them is doubled, how does the electric potential energy of the system change?

A) It is doubled.

B) It is quadrupled.

C) It is halved.

D) It is quartered.

Correct Answer: C

The electric potential energy is given by U_E = k * (q1*q2) / r. Since the energy is inversely proportional to the distance 'r', doubling the distance (2r) will cause the potential energy to become half of its original value.

A system consists of three point charges: qA, qB, and qC. According to the provided principles, how is the total electric potential energy of this system calculated?

A) By calculating the energy of the strongest interaction only.

B) By summing the potential energies of the pairs (qA, qB), (qA, qC), and (qB, qC).

C) By averaging the potential energies of all three charges with respect to a reference point.

D) By multiplying the individual potential energies of the three pairs.

Correct Answer: B

The content states that the total electric potential energy is determined by finding the sum of the electric potential energies of the individual interactions between each pair of charged objects. For three charges, there are three unique pairs.

Consider a system with one positively charged object (+q) and one negatively charged object (-q). What is the sign of the electric potential energy of this system?

A) Positive

B) Negative

C) Zero

D) It cannot be determined without knowing the distance.

Correct Answer: B

Using the formula U_E = k * (q1*q2) / r, the product of the charges is (+q) * (-q) = -q^2. Since k, q^2, and r are all positive, the resulting potential energy will be negative.

In the equation U_E = k * (q1*q2) / r, what does the term 'k' represent?

A) The kinetic energy of the system.

B) A proportionality constant (1 / 4πε₀).

C) The distance between the charges.

D) The magnitude of the smaller charge.

Correct Answer: B

The provided content defines the electric potential energy equation as U_E = (1 / 4πε₀) * (q1*q2) / r = k * (q1*q2) / r, explicitly showing that 'k' is the constant 1 / 4πε₀.

The electric potential energy between two charges, q1 and q2, is U_E. If the magnitude of q1 is doubled and the magnitude of q2 is tripled, while the distance r remains constant, what is the new potential energy of the system?

A) 2 * U_E

B) 3 * U_E

C) 5 * U_E

D) 6 * U_E

Correct Answer: D

The original energy is U_E = k * (q1*q2) / r. The new charges are 2*q1 and 3*q2. The new energy is U_new = k * ((2*q1)*(3*q2)) / r = 6 * (k * (q1*q2) / r) = 6 * U_E.

What condition would result in an electric potential energy of zero between two charged objects, q1 and q2, assuming they are a finite distance apart?

A) The charges must be equal in magnitude.

B) The charges must be opposite in sign.

C) The distance 'r' approaches infinity.

D) The product of the charges (q1*q2) is positive.

Correct Answer: C

In the equation U_E = k * (q1*q2) / r, for U_E to be zero, either the numerator (q1*q2) must be zero or the denominator 'r' must approach infinity. The question assumes charges exist, so the standard reference point for zero potential energy is when the charges are infinitely far apart.

A system's total electric potential energy is calculated by summing the energies of all unique pairs of charges. If a system has four distinct point charges, how many individual energy interactions must be calculated and summed?

A) 3

B) 4

C) 6

D) 12

Correct Answer: C

For a system of four charges (1, 2, 3, 4), one must find the energy for each unique pair. The pairs are (1,2), (1,3), (1,4), (2,3), (2,4), and (3,4). This results in a total of 6 interactions to be summed.

Two charges, +q and +2q, have an initial potential energy U_E when separated by a distance r. If the distance between them is reduced to r/3, what is the new potential energy in terms of U_E?

A) U_E / 3

B) U_E / 9

C) 3 * U_E

D) 9 * U_E

Correct Answer: C

The initial energy is U_E = k * (q * 2q) / r. The new energy is U_new = k * (q * 2q) / (r/3). Dividing by r/3 is the same as multiplying by 3/r. Therefore, U_new = 3 * [k * (q * 2q) / r] = 3 * U_E.