Question

A charge particle of charge $q$ is moving with speed $v$ in a circle of radius $R$ as shown in figure. Then the magnetic field at a point on axis of circle at a distance $x$ from centre is :

• A. $\frac{{\mu }_0}{4\pi }\frac{qV}{R^2}$
• B. $\frac{{\mu }_0}{4\pi }\frac{qV}{(R^2+x^2)}$
• C. $\frac{{\mu }_0}{4\pi }\frac{qV}{x^2}$
• D. $\frac{{\mu }_0}{4\pi }\frac{qVR}{(R^2+x^2{)}^{3/2}}$

Answer 1

The correct option is D $\frac{{\mu }_0}{4\pi }\frac{qVR}{(R^2+x^2{)}^{3/2}}$

Charge $q$ moving in a circle gives rise to a current $I=\frac{q}{\frac{2\pi R}{v}}=\frac{qv}{2\pi R}$
The magnetic field on the axis at a distance $x$ from the center of a current carrying circular loop of radius $R$ is:
$B_{axis}=\frac{{\mu }_{0}I{R}^2}{2(R^2+x^2{)}^{\frac{3}{2}}}=\frac{{\mu }_0\frac{qv}{2\pi R}{R}^2}{2(R^2+x^2{)}^{\frac{3}{2}}}=\frac{{\mu }_{0}qvR}{4\pi (R^2+x^2{)}^{\frac{3}{2}}}$