A current-carrying circular loop of radius 'R | vedclass

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(A) The magnetic field at the centre of a circular loop of radius $R$ carrying current $I_C$ is given by $B_C = \frac{\mu_0 I_C}{2R}$.The magnetic fie

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$\frac{R I_w}{\pi I_C}$

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(A) The magnetic field at the centre of a circular loop of radius $R$ carrying current $I_C$ is given by $B_C = \frac{\mu_0 I_C}{2R}$.The magnetic field at a distance $d$ from a long straight wire carrying current $I_w$ is given by $B_w = \frac{\mu_0 I_w}{2 \pi d}$.For the net magnetic field at the centre of the loop to be zero,the magnitudes of the magnetic fields produced by the loop and the wire must be equal and opposite in direction.Thus,$B_C = B_w$.$\frac{\mu_0 I_C}{2R} = \frac{\mu_0 I_w}{2 \pi d}$.Canceling $\mu_0$ and $2$ from both sides,we get $\frac{I_C}{R} = \frac{I_w}{\pi d}$.Solving for $d$,we get $d = \frac{R I_w}{\pi I_C}$.

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