Electric Potential Energy and Potential — Practice Quiz

A Physics cheat sheet for Electric Potential Energy and Potential — every key formula with its symbols defined — plus a medium-level practice quiz to test recall.

Formulas & key concepts

Work and Potential Energy: Work \(W_{AB}\) done by electric force as charge moves from A to B equals change in electric potential energy \(EPE\).

$$W_{AB} = EPE_A - EPE_B$$

Electric Potential Definition: Electric potential \(V\) is the electric potential energy \(EPE\) per unit charge \(q_0\).

$$V = \frac{EPE}{q_0}$$

Potential Difference: Difference in potential between points B and A is related to work done by electric force.

$$V_B - V_A = \frac{-W_{AB}}{q_0}$$

Potential of a Point Charge: Electric potential \(V\) at distance \(r\) from a point charge \(q\).

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

Capacitor Charge: Charge \(q\) on a capacitor is proportional to potential difference \(V\) across it. \(C\) is capacitance.

$$q = CV$$

Parallel Plate Capacitor: Capacitance \(C\) depends on area \(A\), separation \(d\), and dielectric constant \(\kappa\).

$$C = \frac{\kappa \epsilon_0 A}{d}$$

Where: \(\epsilon_0\) = permittivity of free space

Energy Stored in Capacitor: Potential energy stored in a charged capacitor.

$$Energy = \frac{1}{2}CV^2 = \frac{1}{2}qV = \frac{q^2}{2C}$$

Practice quiz

  1. If the electric potential energy of a $2 \text{ C}$ charge at point A is $10 \text{ J}$ and at point B is $4 \text{ J}$, what is the potential difference $V_B - V_A$?

    • $3 \text{ V}$
    • $-3 \text{ V}$
    • $7 \text{ V}$
    • $-7 \text{ V}$

    Answer: $-3 \text{ V}$

  2. What is the electric potential at a distance of $0.5 \text{ m}$ from a point charge of $4 \times 10^{-9} \text{ C}$? (Use $k = 9 \times 10^9 \text{ N} \cdot \text{m}^2/\text{C}^2$)

    • $36 \text{ V}$
    • $72 \text{ V}$
    • $18 \text{ V}$
    • $144 \text{ V}$

    Answer: $72 \text{ V}$

  3. A capacitor stores $6 \times 10^{-6} \text{ C}$ of charge when connected to a $12 \text{ V}$ battery. What is its capacitance?

    • $0.5 \mu \text{F}$
    • $2 \mu \text{F}$
    • $72 \mu \text{F}$
    • $1.2 \mu \text{F}$

    Answer: $0.5 \mu \text{F}$

  4. A parallel plate capacitor has plates of area $0.02 \text{ m}^2$ separated by $0.001 \text{ m}$. If a dielectric with $\kappa = 3$ is inserted, what is the capacitance? (Use $\epsilon_0 = 8.85 \times 10^{-12} \text{ F/m}$)

    • $177 \text{ pF}$
    • $531 \text{ pF}$
    • $88.5 \text{ pF}$
    • $265.5 \text{ pF}$

    Answer: $531 \text{ pF}$

  5. How much energy is stored in a $10 \mu \text{F}$ capacitor charged to a potential difference of $20 \text{ V}$?

    • $1 \text{ mJ}$
    • $2 \text{ mJ}$
    • $4 \text{ mJ}$
    • $0.5 \text{ mJ}$

    Answer: $2 \text{ mJ}$

  6. A point charge $q_1 = 3 \times 10^{-9} \text{ C}$ creates an electric potential. If a second charge $q_2 = 2 \times 10^{-9} \text{ C}$ is placed at a point where the potential due to $q_1$ is $18 \text{ V}$, what is the electric potential energy of $q_2$ at that point?

    • $6 \text{ nJ}$
    • $12 \text{ nJ}$
    • $36 \text{ nJ}$
    • $54 \text{ nJ}$

    Answer: $36 \text{ nJ}$

  7. A positive charge moves from point A to point B. If the electric force does positive work $W_{AB}$ during this movement, which of the following statements is true?

    • $EPE_B - EPE_A > 0$ and $V_B - V_A > 0$
    • $EPE_B - EPE_A < 0$ and $V_B - V_A < 0$
    • $EPE_B - EPE_A > 0$ and $V_B - V_A < 0$
    • $EPE_B - EPE_A < 0$ and $V_B - V_A > 0$

    Answer: $EPE_B - EPE_A < 0$ and $V_B - V_A < 0$

  8. To increase the capacitance of a parallel plate capacitor, which of the following actions would be effective?

    • Decrease the area of the plates.
    • Increase the distance between the plates.
    • Insert a dielectric material with a dielectric constant $\kappa > 1$.
    • Decrease the dielectric constant of the material between the plates.

    Answer: Insert a dielectric material with a dielectric constant $\kappa > 1$.

  9. A capacitor is charged and then disconnected from the battery. If the distance between its plates is doubled, how does the energy stored in the capacitor change?

    • It remains the same.
    • It doubles.
    • It halves.
    • It quadruples.

    Answer: It doubles.

  10. A $5 \mu \text{F}$ capacitor stores $1 \text{ mJ}$ of energy. What is the charge stored on its plates?

    • $50 \mu \text{C}$
    • $100 \mu \text{C}$
    • $200 \mu \text{C}$
    • $250 \mu \text{C}$

    Answer: $100 \mu \text{C}$

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