Question

Two circular coils made up of identical wires of length 40 cm have respectively 18 and 9 turns and the current flowing through the second coil is 4 times the current through 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

The correct option is D 1:2

The Magnetic induction at the centre of circular coil,

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

for $N$ number of turns of coil,

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

The two circular coils made up of two identical wire of length $40cm$

The perimeter of circle is $P=2\pi r$ perimeter is same so, radius of both circular coil is same.

The magnetic induction ,

$B\alpha NI$

$N_1=18,I_1=IA$

$N_2=9,I_2=4IA$

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

$=\frac{18\times I}{9\times 4I}=\frac{1}{2}$

$B_1:B_2=1:2$