Question

A direct current is passing through a wire. It is bent to form a coil of one turn. Now, it is further bent into a coil of $4$ turns but of smaller radius. The ratio of magnetic induction at the centre of this to the magnetic induction at the centre of coil of one turn is

• A. 4.00
• B. 4
• C. 4.0

Answer 1

Answer: (A), (B), (C)

The magnetic induction at the centre of a circular coil carrying current $I$ is, $B=\frac{{\mu }_{0}I}{2R}$

I case: One turn
$L=2\pi R_1,B_1=\frac{{\mu }_{0}I}{2R_1}=\frac{{\mu }_{0}I\left[2\pi \right]}{2L}$

II case: Four turns
$L=4\left[2\pi R_2\right],B_2=\frac{{\mu }_{0}I}{2R_2}=\frac{{\mu }_{0}I\left[8\pi \right]}{2L}$

We need, $\frac{B_2}{B_1}=\frac{8}{2}=4$