When a long wire carrying a steady current is best into a circular coil of one turn, the magnetic induction at its centre is B. When the same wire carrying the same current is bent into a circular coil of one turn, the magnetic induction at its centre is B. when the same wire carrying the same current is bent to form a circular coil of a turns of a smaller radius, the magnetic induction at the centre will be

Options

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

Answer

D

Explanation

Let I be current and l be the length of the wire .
Ist case : `B=(mu_0In)/(2r) = (mu_0Ixxpi)/l` where `2pir=l`
and n = 1
For Iind case : `l=n(2pir.)impliesr.=l/(2npi)`
`B.=(mu_0nI)/(2r.)=(mu_0nI)/(2(l)/(2npi))=(n^2mu_0piI)/l=n^2B`