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(A) The magnetic field at the centre of a semicircular arc of radius $R$ carrying current $I$ is given by $B = \frac{\mu_0 I}{4R}$.In the given figure

Vedclass · Accepted Answer

$\frac{\mu_0 I}{4}\left(\frac{1}{R_1}+\frac{1}{R_2}\right)$

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(A) The magnetic field at the centre of a semicircular arc of radius $R$ carrying current $I$ is given by $B = \frac{\mu_0 I}{4R}$.In the given figure,the currents in the two semicircular arcs flow in the same sense (clockwise) relative to the centre $O$.Therefore,the magnetic fields produced by both arcs at the centre $O$ are in the same direction (into the plane of the paper).The total magnetic field at the centre $O$ is the sum of the individual magnetic fields:$B_{	ext{net}} = B_1 + B_2$$B_{	ext{net}} = \frac{\mu_0 I}{4R_1} + \frac{\mu_0 I}{4R_2}$$B_{	ext{net}} = \frac{\mu_0 I}{4} \left( \frac{1}{R_1} + \frac{1}{R_2} ight)$

The figure shows two semicircular loops of radii $R_1$ and $R_2$ carrying current $I$. The magnetic field at the common centre '$O$' is

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