Question

An electric dipole consists of two equal but opposite electric charges, +q and -q, separated by a small distance d. If another charge Q is distance x from the center of the dipole, in the plane perpendicular to the line between +q and -q, and if x W d, the dipole exerts an electric force $F=KqQd/x^3$on charge Q, where K is a constant. How much work does the electric force do if charge Q moves from distance $x_{1}to{x}_2$?

Short answer

Work done by electric force is$W=\frac{KaQd}{2}\left(\frac{{x_2}^2-{x_1}^2}{{x_2}^2{x_1}^2}\right)$

Step-by-step solution

Content Introduction

The work done by variable force is,

$W={\int }_{x_1}^{x_2}Fdx$

Here,$F$is the force,$dx$is small displacement.

Content Explanation

Consider dipole exerts an electric force is $F=\frac{KaQd}{x^3}$

use formula $W={\int }_{x_1}^{x_2}Fdx$to find work done by force F using distance $x_1$to distance.

Use power rule of integral,

Hence work done by electric force is

$W=\frac{KaQd}{2}\left(\frac{{x_2}^2-{x_1}^2}{{x_2}^2{x_1}^2}\right)$