Question

Find the net force acting on the dipole.

• A. $\frac{\partial qQ}{2\pi {\epsilon }_0}\frac{R^2-2x^2}{(R^2+x^2{)}^{5/2}}$
• B. $\frac{\partial qQ}{2\pi {\epsilon }_0}\frac{R^2+2x^2}{(R^2+x^2{)}^{5/2}}$
• C. $\frac{\partial qQ}{2\pi {\epsilon }_0}\frac{R^2-2x^2}{(R^2-x^2{)}^{5/2}}$
• D. $\frac{\partial qQ}{2\pi {\epsilon }_0}\frac{R^2+2x^2}{(R^2-x^2{)}^{5/2}}$

Answer 1

The correct option is A $\frac{\partial qQ}{2\pi {\epsilon }_0}\frac{R^2-2x^2}{(R^2+x^2{)}^{5/2}}$

Distance $=x$ from centre $0$ on the axis of a charged ring of radius $=R$

Charge $=Q$ uniformly distributed

Net force acting on the dipole

dipole $=2qL$

$E=\frac{1}{4\pi {ϵ}_0}\left\{\frac{R^2-{2x}^2}{{(R^2+x^2)}^3/2}\right\}\times \frac{1}{(R^2+x^2)}$

Now, $\frac{2qB}{2\pi {ϵ}_0}\frac{R^2-{2x}^2}{{(R^2+x^2)}^{5/2}}$