Question

Two particles of charges 4 nC and \( Q \) are kept in air with a separation of 10 cm between them. If the electrostatic potential energy of the system is 1.8 μJ, then \( Q \) is:

• A. \( 12 \) nC
• B. \( 9 \) nC
• C. \( 5 \) nC
• D. \( 7 \) nC

Hint:

The electrostatic potential energy depends on the product of charges and the inverse distance between them.

Answer 1

The Correct Option is C

Step 1: Use Electrostatic Potential Energy Formula The electrostatic potential energy between two charges is given by: \[ U = \frac{k q_1 q_2}{r} \] where: 
- \( k = 9 \times 10^9 \) N·m²/C², 
- \( q_1 = 4 \) nC, 
- \( q_2 = Q \), 
- \( r = 10 \) cm \( = 0.1 \) m, 
- \( U = 1.8 \) μJ \( = 1.8 \times 10^{-6} \) J. 
Step 2: Solve for \( Q \) \[ 1.8 \times 10^{-6} = \frac{(9 \times 10^9) (4 \times 10^{-9}) Q}{0.1} \] \[ Q = \frac{1.8 \times 10^{-6} \times 0.1}{(9 \times 10^9) \times (4 \times 10^{-9})} \] \[ Q = 5 \text{ nC} \]