Question

For a point dipole of dipole moment \( \mathbf{p} = p \hat{z} \) located at the origin, which of the following is (are) correct?

• A. The electric field at \( (0, b, 0) \) is zero.
• B. The work done in moving a charge \( q \) from \( (0, 0, b) \) to \( (0, 0, b) \) is \( \frac{qp}{4\pi \epsilon_0 b^2} \).
• C. The electrostatic potential at \( (b, 0, 0) \) is zero.
• D. If a charge \( q \) is kept at \( (0, 0, b) \), it will exert a force of magnitude \( \frac{qp}{4\pi \epsilon_0 b^3} \) on the dipole.

Hint:

The electric field of a dipole decreases with distance and is proportional to \( \frac{1}{r^3} \) at large distances. The work done and potential are related to the interaction between the dipole and charge.

Answer 1

The Correct Option is B, C

Step 1: Understanding the dipole electric field.
The electric field of a dipole varies with distance and direction. The work done in moving a charge \( q \) in the field of a dipole is determined by the interaction between the dipole's electric field and the charge. The work done in moving a charge \( q \) is given by \( \frac{qp}{4\pi \epsilon_0 b^2} \), and the potential at \( (b, 0, 0) \) is zero for the dipole.
Step 2: Conclusion.
Thus, the correct answers are options (B) and (C).