In the figure shown,there are two semicircles | vedclass

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(C) The magnetic field at the center of a semicircular arc of radius $r$ carrying current $i$ is given by $B = \frac{{\mu _0 i}}{{4r}}$.In the given f

Vedclass · Accepted Answer

$\frac{{\mu _0 i}}{4}\left( {\frac{{r_1 + r_2}}{{r_1 r_2}}} \right)$

Vedclass · Answer

(C) The magnetic field at the center of a semicircular arc of radius $r$ carrying current $i$ is given by $B = \frac{{\mu _0 i}}{{4r}}$.In the given figure,there are two semicircular arcs of radii $r_1$ and $r_2$. The current flows in both arcs such that the magnetic field produced by both at the center $O$ is directed into the plane of the paper (using the right-hand thumb rule).Therefore,the total magnetic induction $B$ at the center $O$ is the sum of the magnetic fields due to both arcs:$B = B_1 + B_2$$B = \frac{{\mu _0 i}}{{4r_1}} + \frac{{\mu _0 i}}{{4r_2}}$$B = \frac{{\mu _0 i}}{4} \left( \frac{1}{r_1} + \frac{1}{r_2} \right)$$B = \frac{{\mu _0 i}}{4} \left( \frac{r_1 + r_2}{r_1 r_2} \right)$Thus,the correct option is $C$.

In the figure shown,there are two semicircles of radii $r_1$ and $r_2$ in which a current $i$ is flowing. The magnetic induction at the centre $O$ will be

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