Two circular coils are made of two identical wires of same length and carry same current. If the number of turns of the two coils are 4 and 2, then the ratio of magnetic induction at the centres will be

Options

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

Answer

D

Explanation

Two wires have equal lengths.` therefore L = 2pi r_(1) n_(1) =2pi r_(2) n _(2)`
`therefore (r_(2))/(r_(1))=(n_(1))/(n_(2))=4/2 =2/1" "...(1)`
`and (B_(1))/(B_(2))=(mu_(0))/(4pi) xx(2pi n _(1)I)/(r _(1))xx(4pi)/(mu_(0))xx(r_(2))/(2pi n_(2)I)`
`therefore (B_(1))/(B_(2)) =((n_(1))/(n_92)) ((r_(2))/(r_(1))) =((2)/(1)) xx((2)/(1)) =4/1`