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

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

Test your understanding with short quizzes. This quiz has 16 questions to check your progress.

Question 1 of 16

How is electric potential at a specific point in space formally defined?

All Questions (16)

How is electric potential at a specific point in space formally defined?

A) The electric potential energy per unit charge.

B) The total electric potential energy of a charge configuration.

C) The force experienced per unit charge.

D) The spatial rate of change of the electric field.

Correct Answer: A

Based on the provided content, 'Electric potential describes the electric potential energy per unit charge at a point in space.' Option C describes the electric field.

The electric potential difference between two points, A and B, is best described as the:

A) total work done by the electric field to move a charge from A to B.

B) total change in the system's electric potential energy.

C) change in electric potential energy per unit charge when a test charge is moved between the points.

D) dot product of the electric field and the displacement between the points.

Correct Answer: C

The provided content states, 'The electric potential difference between two points is the change in electric potential energy per unit charge when a test charge is moved between the two points.' This corresponds to the equation ΔV = ΔU_E / q.

If the electric potential V in a region of space is given by the function V(x) = 5x³, where x is in meters and V is in volts, what is the x-component of the electric field, E_x, at x = 2 m?

A) 40 V/m

B) -40 V/m

C) 60 V/m

D) -60 V/m

Correct Answer: D

According to the provided content, the component of the electric field is the negative of the spatial rate of change of the potential: E_x = -dV/dx. The derivative of V(x) = 5x³ is dV/dx = 15x². Therefore, E_x = -15x². At x = 2 m, E_x = -15(2)² = -15(4) = -60 V/m.

Which statement best describes the geometric relationship between electric field vectors and equipotential lines?

A) Electric field vectors are always parallel to equipotential lines.

B) Electric field vectors are always perpendicular to equipotential lines.

C) The angle between electric field vectors and equipotential lines is always 45 degrees.

D) Electric field vectors and equipotential lines are unrelated geometric concepts.

Correct Answer: B

The content states that 'Electric field vector maps and equipotential lines are tools to describe the field'. The fundamental relationship, derived from E_x = -dV/dx, is that the electric field (representing the direction of steepest potential change) must be perpendicular to the lines of constant potential (equipotential lines).

When using the equation V = (1/4πε₀)∫(dq/r) to find the electric potential due to a continuously charged object, what does the integration process accomplish?

A) It calculates the total charge of the object.

B) It finds the average distance from the object to the point of interest.

C) It sums the potential contributions from all infinitesimal charge elements (dq) of the object.

D) It determines the direction of the electric field.

Correct Answer: C

The provided content states that 'Expressions for the electric potential of charge distributions can be found using integration and the principle of superposition.' The integral sums up the potential contributions (dV = k*dq/r) from every infinitesimal charge element 'dq' that makes up the entire object.

A point P is located 2m from a charge +Q and 2m from a charge -Q. To find the total electric potential at point P, one must:

A) vectorially add the potentials from each charge.

B) algebraically sum the potentials from each charge.

C) use only the potential from the positive charge.

D) multiply the magnitudes of the two potentials.

Correct Answer: B

The content mentions using the 'principle of superposition' for charge distributions. Since electric potential is a scalar quantity, the total potential at a point is the simple algebraic sum of the potentials due to each individual charge. In this case, V_total = V_{+Q} + V_{-Q} = kQ/2 + k(-Q)/2 = 0.

An equipotential map shows a region where the equipotential lines are spaced very far apart. This indicates that in this region:

A) the electric field is strong.

B) the electric potential is changing rapidly.

C) the electric potential is high.

D) the electric field is weak.

Correct Answer: D

The relationship E_x = -dV/dx indicates that the magnitude of the electric field is equal to the spatial rate of change of potential. If equipotential lines are far apart, it means the potential (V) changes very little over a large distance (dx), so the rate of change (dV/dx) is small. This corresponds to a weak electric field.

What is the physical meaning of the dot product, E⋅dr, within the integral ΔV = -∫E⋅dr?

A) It isolates the component of the electric field that is perpendicular to the path element dr.

B) It calculates the total work done by the electric field over the entire path.

C) It represents the contribution to the potential change from moving along the infinitesimal path element dr.

D) It ensures that the result of the integration is a vector quantity.

Correct Answer: C

The dot product E⋅dr calculates the component of the electric field parallel to the infinitesimal displacement dr, multiplied by the magnitude of dr. This product represents the small change in potential, dV, that occurs when moving along that tiny path segment. The integral then sums all these small changes to find the total potential difference.

According to the provided content, how will a positive test charge, released from rest in an electric field, initially move relative to the field lines and equipotential surfaces?

A) It will move parallel to an equipotential line.

B) It will move in the direction of a local electric field line.

C) It will move in the direction opposite to a local electric field line.

D) It will remain stationary regardless of the field.

Correct Answer: B

The content states that 'electric field vector maps... can be used to predict the motion of charged objects'. The electric field vector represents the direction of the force on a positive charge. Therefore, a positive charge released from rest will accelerate and move in the direction of the electric field line at that point.

If the potential difference between point A and point B is ΔV = +20 V, what is the change in electric potential energy, ΔU_E, for a charge of q = -2 C moved from A to B?

A) -40 J

B) +40 J

C) -10 J

D) +10 J

Correct Answer: A

The content provides the relationship ΔV = ΔU_E / q. Rearranging this gives ΔU_E = q * ΔV. Substituting the given values: ΔU_E = (-2 C) * (+20 V) = -40 J.

What is the physical significance of the negative sign in the relationship E_x = -dV/dx?

A) It indicates that electric potential is always a negative value.

B) It signifies that the electric field vector points in the direction of decreasing electric potential.

C) It is a reminder that the electric field is a conservative force.

D) It ensures that the units for electric field (N/C) and potential (V) are consistent.

Correct Answer: B

The relationship E_x = -dV/dx means that the electric field component in a direction is the negative of the potential's rate of change in that direction. If potential V increases with x (positive dV/dx), the field E_x is in the negative x-direction. This means the electric field always points 'downhill' from higher potential to lower potential.

Which statement best contrasts the nature of electric potential and electric field?

A) Both are vector quantities, but potential relates to energy and field relates to force.

B) Potential is a scalar quantity related to energy per charge, while the field is a vector quantity related to force per charge.

C) Both are scalar quantities, but the field is the derivative of the potential.

D) Potential is a property of a single charge, while the field requires at least two charges.

Correct Answer: B

The content defines potential as potential energy per unit charge (a scalar concept, V) and implies the field is a force-related concept (a vector, E). The equations E_x = -dV/dx and ΔV = -∫E⋅dr explicitly show the scalar (V) and vector (E) relationship, where the field is related to the spatial change in the potential.

The equation ΔV = V_b - V_a = -∫E⋅dr implies that the potential difference between two points in a static electric field is independent of the path taken. Why must this be true?

A) Because the displacement vector dr is always a straight line.

B) Because the electric field E is uniform throughout space.

C) Because the potential at any given point (like V_a or V_b) has a single, well-defined value.

D) Because the dot product E⋅dr is always zero for any closed loop.

Correct Answer: C

The content defines electric potential as the energy per unit charge 'at a point in space'. This means V_a and V_b are fixed values for those specific points. Their difference, ΔV, must therefore also be a fixed, unique value. The integral is simply the method for calculating this pre-determined difference, so the result of the integral cannot depend on the path chosen.

An electron (a negatively charged particle) is released from rest in a region with the electric potential shown by equipotential lines. The electron will experience a force that directs it:

A) from a region of higher potential to a region of lower potential.

B) from a region of lower potential to a region of higher potential.

C) along a path of constant potential.

D) in a direction perpendicular to the electric force.

Correct Answer: B

The content allows for predicting motion. The electric field points from higher potential to lower potential. The force on a positive charge is in the direction of the field. Since an electron is negatively charged, the force on it is in the opposite direction of the electric field. Therefore, an electron is pushed from a region of lower potential toward a region of higher potential.

The principle of superposition, when applied to electric potential from multiple point charges, states that the total potential is the:

A) vector sum of the individual potentials.

B) algebraic sum of the individual potentials.

C) average of the individual potentials.

D) product of the individual potentials.

Correct Answer: B

The content states that 'Expressions for the electric potential of charge distributions can be found using... the principle of superposition.' Since potential is a scalar, superposition means you simply add the values from each charge together, taking their positive or negative signs into account. This is an algebraic sum.

How much work is done by the electric field when a +5 C charge is moved from point X to point Y, if both points lie on the same 100V equipotential line?

A) 500 J

B) -500 J

C) 0 J

D) It depends on the distance between X and Y.

Correct Answer: C

An equipotential line is a line of constant potential. Therefore, the potential difference between points X and Y is ΔV = V_Y - V_X = 100V - 100V = 0. The change in potential energy is given by ΔU_E = qΔV. Since ΔV = 0, the change in potential energy is 0. The work done by the conservative electric field is W_E = -ΔU_E, which is also 0.