AP Physics 2 Electric Potential and Capacitors

« Back to AP Physics Guide / Unit 10 Part 1: Charge & Force

Visual summary of electric potential energy, voltage levels, and a parallel plate capacitor.

While Part 1 focused on Force (a vector), Part 2 focuses on Energy (a scalar). Understanding Electric Potential is key to mastering how charges move through circuits and store energy in electronic components like capacitors.

1. Electric Potential Energy vs. Potential

In AP Physics 2, we distinguish between the energy of a specific charge ( $U_E$ ) and the “potential” of a location in space ( $V$ ).

Electric Potential Energy ( $U_E$ ): The energy a charge possesses due to its position in an electric field.
Electric Potential ( $V$ ): Often called Voltage, this is the potential energy per unit charge ( $V = U_E / q$ ).

$\Delta V = \dfrac{\Delta U_E}{q} \quad \text{and} \quad V = k \dfrac{q}{r}$

Potential is a scalar! You simply add the voltages from different charges without using vectors.

2. Capacitors

A capacitor is a device used to store electric charge and energy. The most common type on the exam is the Parallel Plate Capacitor.

Parallel plate capacitor showing uniform electric field between charged plates

Storing Charge: Capacitance ( $C$ ) depends only on the geometry of the plates—their area ( $A$ ) and separation distance ( $d$ ).

$C = \epsilon_0 \dfrac{A}{d} \quad \text{and} \quad Q = CV$

$Q$ : Stored Charge | $C$ : Capacitance (Farads) | $V$ : Potential difference.

$U_C = \dfrac{1}{2}CV^2 = \dfrac{1}{2}QV = \dfrac{Q^2}{2C}$

Energy stored in a charged capacitor (all three forms are equivalent)

3. Conservation of Electric Energy

Just like a falling ball converts gravitational potential energy into kinetic energy, a charge moving through a potential difference converts electric potential energy into kinetic energy.

$K_i + U_{Ei} = K_f + U_{Ef}$

Total mechanical energy is conserved in the absence of external work.

4. Quick AP Practice

📚 Unit 10 Mastery Challenge

1. If you double the area of the plates in a parallel plate capacitor, what happens to its capacitance?

Check Answer

Since $C \propto A$ , doubling the area doubles the capacitance ( $2C$ ).

2. An electron is accelerated from rest through a potential difference of $100 \, \text{V}$ . Does it gain or lose potential energy?

Check Answer

A negative charge (electron) moving toward a higher potential loses potential energy (it converts it to kinetic energy).

3. A capacitor stores $10 \, \mu\text{C}$ of charge at $20 \, \text{V}$ . How much energy is stored?

Check Answer

Using $U_C = \frac{1}{2}QV = \frac{1}{2}(10 \times 10^{-6})(20) = \mathbf{100 \, \mu\text{J}}$ .

AP Physics 2: Electric Potential and Capacitors

1. Electric Potential Energy vs. Potential

2. Capacitors

3. Conservation of Electric Energy

4. Quick AP Practice

📚 Unit 10 Mastery Challenge

🔗 Related AP Physics 2 Resources