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(D) The magnetic field at the centre of a circular loop of radius $r$ carrying current $i$ is given by $B = \frac{\mu_0 i}{2r}$.For the smaller loop o

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(D) The magnetic field at the centre of a circular loop of radius $r$ carrying current $i$ is given by $B = \frac{\mu_0 i}{2r}$.For the smaller loop of radius $r_1$ and current $i_1$,the magnetic field is $B_1 = \frac{\mu_0 i_1}{2r_1}$.For the larger loop of radius $r_2$ and current $i_2$,the magnetic field is $B_2 = \frac{\mu_0 i_2}{2r_2}$.Since the currents are in opposite directions,the net magnetic field at the centre is $B = |B_1 - B_2| = \frac{\mu_0}{2} |\frac{i_1}{r_1} - \frac{i_2}{r_2}|$.According to the problem,$B = \frac{1}{2} B_1$.Substituting the expressions: $\frac{\mu_0}{2} |\frac{i_1}{r_1} - \frac{i_2}{r_2}| = \frac{1}{2} (\frac{\mu_0 i_1}{2r_1})$.$|\frac{i_1}{r_1} - \frac{i_2}{r_2}| = \frac{i_1}{2r_1}$.Given $r_2 = 2r_1$,we have $\frac{i_1}{r_1} - \frac{i_2}{2r_1} = \frac{i_1}{2r_1}$ (assuming $B_1 > B_2$ for the net field to be positive).$\frac{i_1}{2r_1} = \frac{i_2}{2r_1}$,which implies $i_1 = i_2$.Therefore,$i_2/i_1 = 1$.

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