Question

Two point dipoles \( \mathbf{p_k} \) and \( \mathbf{L_k} \) are located at \( (0,0,0) \) and \( (1m, 0, 2m) \) respectively. The resultant electric field due to the two dipoles at the point \( (1m, 0, 0) \) is

• A. \( \frac{9p}{32 \pi \epsilon_0} \hat{k} \)
• B. \( \frac{7p}{32 \pi \epsilon_0} \hat{k} \)
• C. \( \frac{7p}{32 \pi \epsilon_0} \hat{i} \)
• D. \( \frac{-7p}{32 \pi \epsilon_0} \hat{k} \)

Hint:

The electric field due to a dipole decreases as the cube of the distance from the dipole.

Answer 1

The Correct Option is A

Step 1: Electric Field Due to Dipole.
The electric field due to a dipole at a distance \( r \) from its center is given by: \[ E = \frac{1}{4 \pi \epsilon_0} \frac{2p \cos \theta}{r^3} \] where \( p \) is the dipole moment, \( \theta \) is the angle between the line joining the observation point and the dipole axis, and \( r \) is the distance from the dipole.
Step 2: Conclusion.
The correct answer is (A), \( \frac{9p}{32 \pi \epsilon_0} \hat{k} \).