The electric current in a circular coil of two turns produced a magnetic induction of 0.2 T at its centre. The coil is unwound and then rewound into a circular coil of four turns. If same current flows in the coil, the magnetic induction at the centre of the coil now is

Options

A. `0.4` T
B. `0.8T `
C. `1.2` T
D. `1.6` T

Answer

D

Explanation

`B=(mu_(0))/(4pi)((2pini)/(r))`
`therefore` For same` , B prop n/r`
In this case, `n_(2) =4n_(1)`
`because` The length of the coil remains constant
`therefore L =2pir_(1) =4 (2pir_(2)) therefore r_(1) =4r_(2) or r_(2) =(r_(1))/(4)`
`therefore(B_(2))/(B_(1))=((n_(2))/(n_(1)))((r_(1))/(r_(2)))=4xx4=16`
`therefore B_(2) =16B_(1) =16 xx0.1 =1.6T`