Question

The magnetic field intensity $\overrightarrow{H}$ at the centre of current carrying loop (circular in space) and kept in x -y plane as shown will be

• A. $\frac{I}{2R}\widehat{a_z}$
• B. $-\frac{I}{2R}\widehat{a_z}$
• C. $\frac{I}{R}\widehat{a_z}$
• D. $-\frac{I}{R}\widehat{a_z}$

Answer 1

The correct option is A $\frac{I}{2R}\widehat{a_z}$

We know,

Biot Savart's law, $H=\int \frac{I\overrightarrow{dI}\times \widehat{a_r}}{4\pi R^2}={\int }_0^{2\pi }\frac{IRd\varphi \widehat{a_{\varphi }}}{4\pi R^2}\left(\widehat{-a_{\rho }}\right)$

=$\frac{I}{4\pi }{\int }_0^{2\pi }\frac{Rd\varphi }{R^2}\left(\widehat{a_z}\right)=\frac{I}{2R}\widehat{a_z}$