Solved Examples of Electric Potential: A Detailed Problem-Solving Guide

📚 Quick Study Guide

• ⚡ Electric potential (V) is the amount of work needed to move a unit positive charge from a reference point to a specific point inside the electric field. Measured in Volts (V).
• ➗ Formula for electric potential due to a point charge: $V = \frac{kQ}{r}$, where $k = 8.99 \times 10^9 Nm^2/C^2$ (Coulomb's constant), Q is the charge, and r is the distance from the charge.
• ➕ The electric potential due to multiple point charges is the scalar sum of the potentials due to each charge individually: $V_{total} = V_1 + V_2 + V_3 + ...$
• 🚧 Electric potential energy (U) is the potential energy a charge possesses due to its location in an electric field: $U = qV$, where q is the charge and V is the electric potential at that location.
• 📉 Electric field and electric potential are related by: $E = -\frac{dV}{dr}$, where E is the electric field and dV/dr is the rate of change of potential with respect to distance. In simpler terms, electric field points in the direction of decreasing potential.
• 💡 Remember that electric potential is a scalar quantity, so direction doesn't matter when summing potentials from multiple charges.

🧪 Practice Quiz

1. What is the electric potential at a distance of 0.5 m from a point charge of $2 \times 10^{-6}$ C?

   1. 18,000 V
   2. 36,000 V
   3. 9,000 V
   4. 72,000 V

2. Two charges, +q and -q, are separated by a distance d. What is the electric potential at the midpoint between the charges?

   1. $k(2q)/d$
   2. $0$
   3. $k(q)/d$
   4. $k(q)/(2d)$

3. If the electric potential at a point is 100 V, how much work is required to bring a charge of 0.1 C from infinity to that point?

   1. 1 J
   2. 10 J
   3. 100 J
   4. 0.1 J

4. The electric potential at a certain point is 500 V. If a charge of -2 C is placed at that point, what is its electric potential energy?

   1. 1000 J
   2. -1000 J
   3. 250 J
   4. -250 J

5. What is the electric potential at the center of a square with side 'a' having equal charges 'q' at each corner?

   1. $4kq/a$
   2. $2\sqrt{2}kq/a$
   3. $kq/a^2$
   4. $0$

6. A uniform electric field of 200 V/m is directed along the positive x-axis. What is the potential difference $V_B - V_A$ between point A (0, 0) and point B (4 m, 0)?

   1. 800 V
   2. -800 V
   3. 200 V
   4. -200 V

7. Which of the following statements is true regarding electric potential?

   1. Electric potential is a vector quantity.
   2. Electric potential is constant in the direction of the electric field.
   3. Electric potential is a scalar quantity.
   4. Electric potential is measured in Newtons.