Question

Find work done in moving a 2\mu C charge from A to B.

• A. 6 \mu J
• B. 120 mJ
• C. 34.3 \mu J
• D. 24.2 \mu J

Hint:

To calculate work done in moving a charge, use the potential difference and the magnitude of the charge.

Answer 1

The Correct Option is C

Step 1: Use the formula for work done by electric field.
The work done \( W \) in moving a charge \( q \) in an electric field \( E \) is: \[ W = U_2 - U_1 \] Where \( U_1 \) and \( U_2 \) are the potential energies at points A and B, respectively. The potential energy is given by: \[ U = q \cdot V \] Where \( V \) is the potential.
Step 2: Calculate the work done.
Given \( q = 2 \, \mu \text{C} = 2 \times 10^{-6} \, \text{C} \), and \( Z_1 = 10 \, \text{C} \), the potential difference between A and B is: \[ W = (2 \times 10^{-6} \times 9 \times 10^9 \times 10) \left( \frac{1}{3} - \frac{1}{7} \right) \] \[ W = 34.3 \, \mu \text{J} \] Step 3: Conclusion.
The work done in moving the charge is 34.3 \mu J, which corresponds to option (3).