Question

A coil of one loop is imade by a wire of length L
and there after a coil of two loops is made by same
wire. The ratio of magnetic field at the centre of
coils respectively :-
(1) 1 : 4 (2) 1:1 (3) 1:8 (4) 4:1
Please answer the question in a systematic manner so that it could be understood.

Answer 1

Answer:

1:4

Explanation:

we know that magnetic induction at center of a wire loop is given as

( mathrm{B}=mu_{0} mathrm{i} / 2 mathrm{r} )

so, in the first case we will have

( B_{1}=frac{mu_{o} i}{2 r_{1}} )

and in the second case as the number of turns is doubled the radius wold be halved as wire length is same

so,( B_{2}=2 times frac{mu_{0} i}{2left(frac{r_{1}}{2}right)} ) so,

the ratio would be ( frac{B_{1}}{B_{2}}=frac{1:4} )