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}