Question

Electric intensity due to an electric dipole varies with distance r as $E\alpha r^n$, where ‘n’ is

• A. $-1$
• B. $-2$
• C. $0$
• D. $-3$

Answer 1

Answer: (D)

Electric field on axis
$E=\frac{kq}{r_1^2}-\frac{kq}{r_2^2}=kq\left(\frac{r_2^2-r_1^2}{r_1^2{r}_2^2}\right)=kq\frac{(r_2-r_1)(r_1+r_2)}{r_1^2{r}_2^2}$

$(r_2-r_1)=d{r}_1=r_2=r=\frac{2kqd}{r^3}$

$\therefore E\alpha r^{-3}$
E on radial axis $E_r$
$r>>d$
$E_{net}=\frac{kg}{(r^2+\frac{d^2}{4})}\frac{\frac{d}{2}}{\sqrt{r^2+\frac{d^2}{4}}}=\frac{kq}{(r^2+\frac{d^2}{4})}\frac{\frac{d}{2}}{\sqrt{r^2+\frac{d^2}{4}}}$

$E_r=\frac{kqd}{r^3}$

$\therefore E\alpha r^{-3}$