#AP Physics 2: Electric Potential & Energy - The Night Before ⚡

Hey! Let's get you prepped for the exam. We're going to break down electric potential and energy into bite-sized pieces so you feel confident and ready. Remember, you've got this!

#Electric Potential Difference & Energy Changes

#The Big Idea: Energy & Potential 💡

Electric potential difference is all about how much energy a charged particle gains or loses when it moves between two points. Think of it like a hill for charges – they roll "downhill" from high potential to low potential, gaining or losing kinetic energy as they go. This is crucial for understanding circuits and particle motion.

Key Concept

When a charged object moves between locations with different electric potentials, its electric potential energy changes. This change is directly related to the potential difference and the charge itself.

#Changes in Electric Potential Energy

What happens? When a charged object moves through an electric field, its electric potential energy changes. This is because the electric field does work on the charge.
How to calculate it? Use the formula:

$\Delta U_E = q \Delta V$
- $\Delta U_E$ = Change in electric potential energy (in Joules)
- $q$ = Charge of the object (in Coulombs)
- $\Delta V$ = Electric potential difference (in Volts)
Examples:
- Moving an electron from the negative to the positive terminal of a battery increases its electric potential energy. Think of it as pushing a ball uphill.
- Bringing a positive charge closer to a negative charge decreases its electric potential energy. It's like a ball rolling downhill.

Equipotential lines and electric field lines

Electric field lines (blue) and equipotential lines (red). Charges move along field lines, changing their potential energy.

#Conservation of Energy ⚖️

The Rule: The total energy of a system (electric potential energy + kinetic energy) remains constant. Energy can transform between these forms, but it's never lost or gained.
Energy Exchange:
- If electric potential energy increases, kinetic energy decreases by the same amount. Think of a ball slowing down as it rolls uphill.
- If electric potential energy decreases, kinetic energy increases by the same amount. Think of a ball speeding up as it rolls downhill.
Examples:
- An electron accelerates (gains kinetic energy) as it moves from the negative to the positive terminal in a circuit, because it's losing electric potential energy.
- A proton slows down (loses kinetic energy) as it approaches a positively charged nucleus, because it's gaining electric potential energy.

Memory Aid

Think of a rollercoaster:

Going up the hill (against the field) is like increasing electric potential energy, and you lose speed (kinetic energy).
Going down the hill (with the field) is like decreasing electric potential energy, and you gain speed (kinetic energy).

Exam Tip

Quick Check: If the charge moves with the electric field, its electric potential energy decreases, and it gains kinetic energy. If it moves against the field, its electric potential energy increases, and it loses kinetic energy.

#Final Exam Focus

High-Priority Topics:
- Calculating changes in electric potential energy using $\Delta U_E = q \Delta V$
- Applying the principle of energy conservation to solve problems involving charged particles moving in electric fields.
- Understanding the relationship between electric potential difference and electric fields.
Common Question Types:
- Multiple-choice questions asking about energy changes when a charge moves between two points.
- Free-response questions involving energy conservation in circuits or particle motion.

Common Mistake

Watch Out! Make sure you use the correct sign for the charge ( $q$ ) and the potential difference ( $\Delta V$ ). A negative charge moving to a higher potential will lose potential energy.

Last-Minute Tips:
- Time Management: Quickly identify the core concept in each question. Focus on the given information and what you need to find.
- Common Pitfalls: Double-check your units, especially when converting between energy, charge, and voltage. Remember that potential energy is a scalar quantity, but potential difference can be positive or negative.
- Strategies: Draw diagrams to visualize the situation. Use energy conservation as your go-to tool for solving motion problems.

#Practice Questions

Practice Question

Multiple Choice Questions

A proton moves from a point with a potential of +10 V to a point with a potential of -5 V. What is the change in the proton’s electric potential energy? (A) +15 eV (B) -15 eV (C) +5 eV (D) -5 eV
An electron is released from rest in a uniform electric field. As the electron moves, what happens to its kinetic energy and electric potential energy? (A) Kinetic energy increases, electric potential energy decreases (B) Kinetic energy decreases, electric potential energy increases (C) Both kinetic and electric potential energy increase (D) Both kinetic and electric potential energy decrease

Free Response Question

An electron is accelerated from rest through a potential difference of 500 V.

(a) Calculate the change in electric potential energy of the electron.

(b) Calculate the final kinetic energy of the electron.

(d) If a proton were accelerated through the same potential difference, how would its final speed compare to that of the electron? Explain your reasoning.

Answer Key & Scoring Rubric

Multiple Choice

(B) -15 eV. $\Delta U = q\Delta V = (1e)(-5V - 10V) = -15eV$
(A) Kinetic energy increases, electric potential energy decreases. Electrons move from low to high potential, decreasing potential energy and increasing kinetic energy.

Free Response

(a) (2 points) - 1 point for using the correct formula: $\Delta U = q\Delta V$ - 1 point for the correct answer with units: $\Delta U = (-1.6 \times 10^{-19} C)(500 V) = -8.0 \times 10^{-17} J$

(b) (2 points) - 1 point for recognizing that the change in kinetic energy is equal to the negative change in potential energy: $\Delta KE = -\Delta U$ - 1 point for the correct answer: $\Delta KE = 8.0 \times 10^{-17} J$

(c) (3 points) - 1 point for using the kinetic energy formula: $KE = \frac{1}{2}mv^2$ - 1 point for correctly substituting the mass of an electron - 1 point for the correct answer with units: $v = \sqrt{\frac{2KE}{m}} = \sqrt{\frac{2(8.0 \times 10^{-17} J)}{9.11 \times 10^{-31} kg}} = 1.33 \times 10^{7} m/s$

(d) (3 points) - 1 point for stating that the proton will have a lower final speed - 1 point for stating that kinetic energy gained is the same for both proton and electron - 1 point for explaining that the proton has a much larger mass than the electron, so its speed will be lower for the same kinetic energy

Remember, you've got this! Now go ace that exam! 💪