A current of i ampere is flowing through each | vedclass

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Question

(D) The magnetic field at the center of a circular arc of radius $r$ subtending an angle $	heta$ at the center is given by $B = \frac{\mu_0 i 	heta}

Vedclass · Accepted Answer

$\frac{{{\mu _0}i}}{8}\left( {\frac{1}{R} + \frac{3}{{R'}}} \right)$

Vedclass · Answer

(D) The magnetic field at the center of a circular arc of radius $r$ subtending an angle $	heta$ at the center is given by $B = \frac{\mu_0 i 	heta}{4 \pi r}$.For the arc of radius $R$,the angle subtended is $	heta_1 = \frac{\pi}{2}$ radians. The magnetic field is $B_1 = \frac{\mu_0 i (\pi/2)}{4 \pi R} = \frac{\mu_0 i}{8R}$.For the arc of radius $R'$,the angle subtended is $	heta_2 = \frac{3\pi}{2}$ radians. The magnetic field is $B_2 = \frac{\mu_0 i (3\pi/2)}{4 \pi R'} = \frac{3\mu_0 i}{8R'}$.Since both currents produce magnetic fields in the same direction (into the page),the total magnetic field is $B = B_1 + B_2 = \frac{\mu_0 i}{8R} + \frac{3\mu_0 i}{8R'} = \frac{\mu_0 i}{8} \left( \frac{1}{R} + \frac{3}{R'} ight)$.

$A$ current of $i$ ampere is flowing through each of the bent wires as shown. Find the magnitude of the magnetic field at $O$.

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