AP Physics C Questions on Electric Potential Difference: Exam Prep

📚 Quick Study Guide

• ⚡ Electric Potential Difference (Voltage): The work done per unit charge to move a test charge between two points. Mathematically represented as $V = \frac{W}{q}$, where $V$ is the potential difference, $W$ is the work done, and $q$ is the charge.
• 🔢 Relationship to Electric Field: Electric potential difference is related to the electric field by $V = -\int \vec{E} \cdot d\vec{l}$, where $\vec{E}$ is the electric field and $d\vec{l}$ is the displacement vector. For a uniform electric field, this simplifies to $V = Ed$, where $d$ is the distance between the points.
• 🛡️ Equipotential Surfaces: Surfaces where the electric potential is constant. No work is required to move a charge along an equipotential surface. Electric field lines are always perpendicular to equipotential surfaces.
• 📍 Potential due to a Point Charge: The electric potential at a distance $r$ from a point charge $q$ is given by $V = \frac{kq}{r}$, where $k$ is Coulomb's constant ($k \approx 8.99 \times 10^9 Nm^2/C^2$).
• 💡 Superposition Principle: The electric potential due to a group of point charges is the algebraic sum of the potentials due to each individual charge: $V_{total} = V_1 + V_2 + V_3 + ...$
• 🔋 Capacitors: Devices that store electrical energy. The potential difference across a capacitor is related to the charge stored and the capacitance by $V = \frac{Q}{C}$, where $Q$ is the charge and $C$ is the capacitance.
• 🌍 Units: Electric potential difference is measured in volts (V), where 1 V = 1 J/C.

🧪 Practice Quiz

1. What is the electric potential difference between two points if 60 J of work is required to move a 3 C charge between them?
   1. A) 10 V
   2. B) 20 V
   3. C) 63 V
   4. D) 180 V
2. If the electric potential at a point is 50 V, what is the electric potential energy of a -2 C charge placed at that point?
   1. A) 25 J
   2. B) -25 J
   3. C) 100 J
   4. D) -100 J
3. A uniform electric field of magnitude 200 V/m exists between two parallel plates separated by a distance of 0.5 m. What is the potential difference between the plates?
   1. A) 50 V
   2. B) 100 V
   3. C) 200 V
   4. D) 400 V
4. What is the electric potential at a distance of 0.3 m from a point charge of 5 x 10^-6 C? (Assume k = 9 x 10^9 Nm²/C²)
   1. A) 1.5 x 10^4 V
   2. B) 4.5 x 10^4 V
   3. C) 1.5 x 10^5 V
   4. D) 4.5 x 10^5 V
5. Three point charges are placed along the x-axis: +2q at x = 0, -3q at x = a, and +4q at x = 2a. What is the electric potential at a point infinitely far away?
   1. A) 0
   2. B) kq/a
   3. C) 3kq/2a
   4. D) Insufficient information
6. A parallel-plate capacitor has a capacitance of 5 μF and is charged to a potential difference of 100 V. What is the charge on each plate?
   1. A) 5 x 10^-4 C
   2. B) 5 x 10^-3 C
   3. C) 5 x 10^-2 C
   4. D) 5 x 10^-1 C
7. Which of the following statements is true regarding equipotential surfaces?
   1. A) Work is always required to move a charge along an equipotential surface.
   2. B) Electric field lines are parallel to equipotential surfaces.
   3. C) No work is required to move a charge along an equipotential surface.
   4. D) Equipotential surfaces are always spherical.