GATE 2015 EE – SET 1 Question -12

Solution :

$$\vec{B}$$=$$ \mu _{0}\vec{H}$$

H = $$ H_{1} + H_{2}$$   , where H =$$ \frac{I}2{\pi }R$$

H =$$\frac{I}{2\pi R_{1}} + \frac{I}{2\pi R_{2}}$$

H =  $$\frac{I}{2\pi \left [ \frac{3L}{2} \right ]} + \frac{I}{2\pi \left [ \frac{L}{2} \right ]} $$

H = $$\frac{I}{2\pi }\left [ \frac{2}{3L} + \frac{2}{L} \right ] $$

H = $$ \frac{I}{2\pi }\left [ \frac{6+2}{3L} \right ] $$

H = $$\frac{8I}{\pi 6L}$$ = $$\frac{4I}{\pi 3L}$$ (-az).

$$\vec{B}$$=$$ \mu _{0}\vec{H}$$ = $$ \frac{4\mu_0 I}{3\pi L}(-a_{z})$$ =  $$ \frac{-4\mu 0I}{3\pi L}$$