Question

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

Answer 1

Correct Answer - A
`L=n_12pia_1=n_2 2pi a_2`
`rArr n_1a_1=n_2a_2rArr (a_1)/(a_2)=(n_2)/(n_1)`
Now , `(B_1)/(B_2)=(mu_0 n_1 I//2a_1)/(mu_0n_2I//2a_2)=(n_1)/(n_2)(a_2)/(a_1)`
`therefore (B_1)/(B_2)=((n_1)/(n_2))^2=(4)/(1)` .