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 $B_{loop} = \frac{\mu_0 I_c}{2 R}$.The magnet

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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 $B_{loop} = \frac{\mu_0 I_c}{2 R}$.The magnetic field at a distance $d$ from a long straight wire carrying current $I_w$ is given by $B_{wire} = \frac{\mu_0 I_w}{2 \pi d}$.For the net magnetic field at the centre of the loop to be zero,the magnitudes of these two magnetic fields must be equal and their directions must be opposite:$B_{loop} = B_{wire}$$\frac{\mu_0 I_c}{2 R} = \frac{\mu_0 I_w}{2 \pi d}$Canceling $\mu_0$ and $2$ from both sides:$\frac{I_c}{R} = \frac{I_w}{\pi d}$Solving for $d$:$d = \frac{R I_w}{\pi I_c}$

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