AP Physics C: Electric Potential Multiple Choice Questions

📚 Quick Study Guide

• ⚡ Electric Potential (V): The electric potential at a point is the electric potential energy per unit charge. Measured in volts (V). $V = \frac{U}{q}$
• 📍 Potential Difference ($\Delta V$): The change in electric potential between two points. $\Delta V = V_B - V_A = -\int_A^B \vec{E} \cdot d\vec{l}$
• 💡 Relationship between Electric Field and Potential: The electric field is the negative gradient of the electric potential. $\vec{E} = -\nabla V$ In one dimension: $E = -\frac{dV}{dx}$
• ➕ Potential due to a Point Charge: $V = \frac{kQ}{r}$, where $k = \frac{1}{4\pi\epsilon_0}$ is Coulomb's constant.
• 💪 Work done by Electric Field: The work done by the electric field in moving a charge $q$ from point A to point B is $W = -q\Delta V$.
• ♾️ Electric Potential Energy: The potential energy $U$ of a charge $q$ at a point where the electric potential is $V$ is given by $U = qV$. For a system of two point charges, $U = \frac{k q_1 q_2}{r}$.
• 🛡️ Equipotential Surfaces: Surfaces where the electric potential is constant. Electric field lines are always perpendicular to equipotential surfaces.

🧪 Practice Quiz

1. A point charge +q is placed at the origin. What is the electric potential at a distance r from the origin?
   1. $V = \frac{kq}{r^2}$
   2. $V = kqr$
   3. $V = \frac{kq}{r}$
   4. $V = kqr^2$
2. The electric potential at a certain point in space is 12 V. What is the electric potential energy of a -3$\mu$C charge placed at that point?
   1. -36 $\mu$J
   2. 36 $\mu$J
   3. 4 $\mu$J
   4. -4 $\mu$J
3. The electric field in a region is given by $\vec{E} = (2x\hat{i} + 3y\hat{j})$ N/C. What is the potential difference between the points (0, 0) and (2, 2)?
   1. -10 V
   2. 10 V
   3. -14 V
   4. 14 V
4. Which of the following statements is true about equipotential surfaces?
   1. Electric field lines are parallel to equipotential surfaces.
   2. No work is done in moving a charge along an equipotential surface.
   3. Electric potential is maximum on an equipotential surface.
   4. Electric field is always zero on an equipotential surface.
5. Two point charges, +2q and -q, are placed a distance d apart. At what point on the line connecting them is the electric potential zero?
   1. d/3 from +2q
   2. 2d/3 from +2q
   3. d/3 from -q
   4. 2d/3 from -q
6. A uniform electric field of magnitude 200 V/m is directed along the positive x-axis. A charge of 5 $\mu$C is moved 10 cm along the x-axis. What is the change in potential energy of the charge?
   1. -100 $\mu$J
   2. 100 $\mu$J
   3. -200 $\mu$J
   4. 200 $\mu$J
7. What is the electric potential at the center of a square with side length 'a' if each corner has a charge 'q'?
   1. 0
   2. $\frac{4kq}{a}$
   3. $\frac{4\sqrt{2}kq}{a}$
   4. $\frac{2kq}{a}$