A wire of length l is bent into a circular coil of one turn of radius `R_(1)`. Another wire of the same material and same area of cross-section and same lengths is bent into a circular coil of two turns of radius `R_(2)`. When the same current flows, through the two coils, the ratio of magnetic induction at the centres of the two coils is

Options

A. `1:2`
B. `1:1`
C. `1:4`
D. `3:1`

Answer

C

Explanation

Magnetic induction at the centre of a coil is given by,
`B=(mu_(0)ni)/(2r)`
`Bpropn/R`
`n_(1)=1, n_(2)=2, R_(2)=R_(1)/2`
`(B_(1))/(B_(2))=(n_(1))/(n_(2))xx(R_(2))/(R_(1))`
`implies(B_(1))/(B_(2))=1/2xx(R_(1))/(2R_(1))`
`B_(1):B_(2)=1:4`