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

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$\frac{I_e R}{I_c \pi}$

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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 $B_{loop} = \frac{\mu_0 I_c}{2R}$.The magnetic field at a distance $H$ from a long straight wire carrying current $I_e$ is given by $B_{straight} = \frac{\mu_0 I_e}{2\pi H}$.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.Equating the magnitudes:$\frac{\mu_0 I_c}{2R} = \frac{\mu_0 I_e}{2\pi H}$Solving for $H$:$\frac{I_c}{R} = \frac{I_e}{\pi H}$$H = \frac{I_e R}{\pi I_c}$

$A$ circular loop of a wire and a long straight wire carry currents $I_c$ and $I_e$,respectively,as shown in the figure. Assuming that these are placed in the same plane,the magnetic field will be zero at the centre of the loop when the separation $H$ is:

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