Question

The electric field and the potential of an electric dipole vary with distance 'r' as 

• A. 1/r² and 1/r³
• B. 1/r and 1/r²
• C. 1/r³ and 1/r²
• D. 1/r² and 1/r

Answer 1

The Correct Option is C

Electric Field:

\( E_g = \frac{1}{4 \pi \epsilon_0} \frac{p}{r^3} \sqrt{3 \cos^2 \theta + 1} \)

Electric Potential: 

\( V_g = \frac{1}{4 \pi \epsilon_0} \frac{p \cos \theta}{r^2} \)

Therefore, the correct option is: D.

Answer 2

Given:

\( E = K r^{3/2} \quad \text{and} \quad E \propto r^{3/1} \) 

Similarly, for the potential \( V \), we have:

\( V = K r^2 p \cos \theta \quad \text{and} \quad V \propto r^2 \)

Thus, the relationships show that:

• Energy \( E \) is proportional to \( r^{3/1} \)
• Potential \( V \) is proportional to \( r^2 \)