Question

Two circular coils made up of identical wires of length 40 cm have respectively 8 and 4 turns and the current flowing through the second coil is 4 times greater than in the first coil. The ratio of magnetic induction at their centres is :

• A. 2:3
• B. 3:2
• C. 1:1
• D. 1:2

Answer 1

Answer: (D)

1:2

Two circular coils made up of identical wires of length $40cm$ ,

So, the perimeter of circle is, $P=2\pi r=40cm$

Radius of the circle is, $r=\frac{40cm}{2\pi }$ is same for both circle.

$r_1=r_2=r$ (say)

No. of turns $N_1=8$ First coil

$N_2=4$ second coil

Current in coil, $I_1=Ampere$

$I_2=4IAmpere$

The magnetic induction at the centre of the circular coil,

$B=N\frac{{\mu }_{0}I}{2r}$

Magnetic induction is directly proportional to$NI$

$B\alpha NI$

$\frac{B_1}{B_2}=\frac{N_1{I}_1}{N_2{I}_2}$

$=\frac{8\times I}{4\times 4\times I}$

$=\frac{1}{2}$

$B_1:B_2=1:2$