Question

The magnetic field intensity $\overrightarrow{H}$ at the center of the current of the carrying circular loops shown in the figure below is

• A. $-\frac{I}{R}{\hat{a}}_z$
• B. $-\frac{I}{2R}{\hat{a}}_z$
• C. $\frac{I}{R}{\hat{a}}_z$
• D. $\frac{I}{2R}{\hat{a}}_z$

Answer 1

The correct option is D $\frac{I}{2R}{\hat{a}}_z$

(d)
From Biot savart law,

$\overrightarrow{H}={\int }_0^{2\pi }\frac{IRd\varphi {\hat{a}}_{\varphi }\times (-{\hat{a}}_{\rho })}{4\pi R^2}$

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

$\overrightarrow{H}$ = $\frac{I}{2R}{\hat{a}}_z$