Q. Two circular coils are made of two identical wires of same length. If the number of turns of two coils are 4 and 2, then the ratio of magnetic induction at centres will be zero
A) 4 : 1
B) 2 : 1
C) 1 : 2
D) 1 : 1
Explanation
(a) $L = n_{1}\ 2\pi r_{1} = n_{2}2\pi r_{2}\ \Rightarrow n_{1}r_{1} = n_{2}r_{2}\ \Rightarrow \frac{r_{1}}{r_{2}} = \frac{n_{2}}{n_{1}}$
$B = \frac{\mu_{0}ni}{2r}\ \Rightarrow \frac{B_{1}}{B_{2}} = \ \frac{\mu_{0}n_{1}i/2r_{1}}{\mu_{0}n_{2}i/2r_{2}}$
$= \frac{n_{1}}{n_{2}}.\frac{r_{2}}{r_{1}} = \left( \frac{n_{1}}{n_{2}} \right)^{2} = \frac{1}{4}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.