Q. Two concentric coils of 10 turns each are placed in the same plane. Their radii are 20 cm and 40 cm and carry 0.2 A and 0.3 A current respectively in opposite directions. The magnetic induction (in tesla) at the centre is
A) $\frac{3}{4}\mu_{0}$
B) $\frac{5}{4}\mu_{0}$
C) $\frac{7}{4}\mu_{0}$
D) $\frac{9}{4}\mu_{0}$
Explanation
(b) Two coils carry currents in opposite directions, hence net magnetic field at centre will be difference of the two fields.
$ie,\ \ \ \ B_{net} = \frac{\mu_{0}}{4\pi}\ .\ 2\pi N\left\lbrack \frac{i_{1}}{r_{1}} - \frac{i_{2}}{r_{2}} \right\rbrack$
$= \frac{10\mu_{0}}{2}\left\lbrack \frac{0.2}{0.2} - \frac{0.3}{0.4} \right\rbrack$
$= \frac{5}{4}\mu_{0}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.