Exercises: Electric Potential

Work through each section in order. Show your work for all calculation problems. Pay attention to signs — they carry physical meaning.

Grade 11·21 problems·~30 min·OpenStax Physics (High School)·section·sec-18-4

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Recall / Warm-Up

Which of the following best distinguishes electric potential $V$ from the electric field $E$ ?

$V$ is a scalar (just a number with sign); $E$ is a vector (has direction).

$V$ is a vector and $E$ is a scalar.

$V$ and $E$ are both vectors but point in opposite directions.

$V$ and $E$ are different names for the same physical quantity.

A positive charge is moved opposite to the direction the electric force pushes it. What happens to its electric potential energy?

It increases.

It decreases.

It stays the same.

It becomes zero.

The work done by a constant force $F$ over a displacement $d$ is $W = Fd$ . Which energy principle directly connects this to electric potential energy?

Conservation of energy: work done by the field equals the decrease in electric PE.

Work equals force times time.

The electric field does work only when charge is stationary.

Potential energy is only defined for gravitational forces.

Fluency Practice

The electric potential at a distance $r$ from a point charge $q$ is given by $V = kq/r$ , where $k = 9.0 \times 10^9\ \text{N·m}^2/\text{C}^2$ . What are the SI units of electric potential?

Volts (V) = joules per coulomb (J/C)

Newtons per coulomb (N/C)

Coulombs per meter (C/m)

Joules per meter (J/m)

Diagram showing a point charge +q on the left and a point P at distance r = 0.30 m to the right.

A point charge of $q = +5.0\ \mu\text{C}$ is fixed in space. Calculate the electric potential at a point $r = 0.30\ \text{m}$ from the charge. Use $k = 9.0 \times 10^9\ \text{N·m}^2/\text{C}^2$ .

A point charge of $q = -4.0\ \mu\text{C}$ is fixed in space. What is the electric potential at a distance of $r = 0.20\ \text{m}$ from the charge? Use $k = 9.0 \times 10^9\ \text{N·m}^2/\text{C}^2$ .

A charge of $q = +2.0\ \mu\text{C}$ is moved through a potential difference of $\Delta V = 500\ \text{V}$ (from low to high potential). How much work is done by an external agent in moving the charge?

A charge of $q = -3.0\ \mu\text{C}$ moves from a point at $V_A = 200\ \text{V}$ to a point at $V_B = 500\ \text{V}$ . Calculate the work done by the electric force on this charge.

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