Question

Force of interaction between two co-axial short electric dipoles whose centres are R distance apart varies as

• A. $\frac{1}{R}$
• B. $\frac{1}{R^2}$
• C. $\frac{1}{R^3}$
• D. $\frac{1}{R^4}$

Answer 1

The correct option is D $\frac{1}{R^4}$

$E=\frac{2Kp}{r^3}$
Now the potential energy of a dipole is given by
$U=-p^{{}^{\prime }}Ecos\left(x\right)$
Substituting E and x = 0 since it is co axial
$U=\frac{-2Kp{p}^{{}^{\prime }}}{r^3}F=\frac{-dU}{dr}F=\frac{6Kp{p}^{{}^{\prime }}}{r^4}$