A long wire carries a steady curent . It is bent into a circle of one turn and the magnetic field at the centre of the coil is `B`. It is then bent into a circular loop of `n` turns. The magnetic field at the centre of the coil will be

Options

A. `2n^2B`
B. `nB`
C. `n^2B`
D. `2nB`

Answer

C

Explanation

`B = (mu_0 i)/(2R) = (mu_0 I(2 pi ) )/(2(I) ) = (mu_0pi i)/(l)`
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`B. = (mu_0 "ni")/(2r) = (mu_0"ni")/(2( l)/(2n pi) ) = (n^2 mu_0 pi i)/(l) = n^2 B`