Question

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

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

Answer 1

Answer: (A)

4 : 1

$l=N_{1}2\pi r_1=N_{2}2\pi r_2$

$\frac{r_1}{r_2}=\frac{N_2}{N_1}$...(1)

also $B_1=\frac{{\mu }_{o}NI}{2r}$ ,...(2) current is same for both

using eqation 1 and 2.

$\frac{B_1}{B_2}=\frac{N_1{r}_2}{N_2{r}_1}=\frac{N_2^2}{N_1^2}=16/4=4$