A length lof wire carries a steady current i. It is bent first to form a circular plane coil of one turn . The same length is now bent more sharply to give three loops of smaller radius . The magnetic field at the centre caused by the same current is

Options

A. A quarter of its first value
B. Unaltered
C. Four times of its first value
D. A half of its first value

Answer

C

Explanation

Magnetic field at the centre- `B = (N mu_(0) I)/(2R)`
Case- I : `N_(1) = 1 , 2 pi R = L implies R = (L)/(2pi)`
`B_(1) = (mu_(0) I)/(2. (L//2pi))`
Case - II : `N_(2) = 2 xx 2pi R = L implies R = (L)/(4pi)`
`B_(2) = (2mu_(0) I)/(2(L//4pi))`
`(B_(1))/(B_(2)) = (mu_(0) I)/(2 xx (L //2pi)) * (2 xx (L)/(4pi))/(2mu_(0) I) = (1)/(4) implies B_(2) = 4 B_(1)`