Question

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

• A. $\frac{1}{r}$ and $\frac{1}{r^2}$
• B. $\frac{1}{r^2}$ and $\frac{1}{r}$
• C. $\frac{1}{r^2}$ and $\frac{1}{r^3}$
• D. $\frac{1}{r^3}$ and $\frac{1}{r^2}$

Answer 1

Answer: (D)

$\frac{1}{r^3}$ and $\frac{1}{r^2}$

Electric field and electric potential at a general point at a distance r from the centre of the dipole is

$E_g=\frac{1}{4\pi {ϵ}_o}.\frac{p}{r^3}\sqrt{3{\cos }^2\theta +1}$

And, $V_g=\frac{1}{4\pi {ϵ}_o}.\frac{p\cos \theta }{r^2}$

Hence, D is the correct option.