Q. One of the two identical conducting wires of length L is bent in the form of a circular loop and the other one into a circular coil of N identical turns. If the same current is passed in both, the ratio of the magnetic field at the central of the loop $(B_L)$ to that at the centre of the coil $(B_C)$ , i.e., $R \frac{B_L}{B_C}$ will be

Solution:

$L = 2 \pi R L = N \times2\pi r $
$ R =Nr B_{L} = \frac{\mu_{0} i}{2R} $
$B_{C} = \frac{\mu_{0} Ni}{2r} B_{C} = \frac{\mu_{0} N^{2} i}{2R} $
$\frac{B_{L}}{B_{C}} = \frac{1}{N^{2}} $

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