Q. What is the mutual inductance of a two-loop system as shown with centre separation $l$
A) $\frac{\mu_{0}\pi a^{4}}{8l^{3}}$
B) $\frac{\mu_{0}\pi a^{4}}{4l^{3}}$
C) $\frac{\mu_{0}\pi a^{4}}{6l^{3}}$
D) $\frac{\mu_{0}\pi a^{4}}{2l^{3}}$
Explanation
(d) Magnetic field at the location of coil (2) produced due to coil (1)
$B_{1} = \frac{\mu_{o}}{4\pi}.\frac{2M}{l^{3}}$
Flux linked with coil (2)
$\phi = B_{1}A_{2} = \frac{\mu_{0}}{4\pi}\frac{2i(\pi a^{2})}{l^{3}} \times (\pi a^{2})$
Also $\phi_{2} = Mi \Rightarrow M = \frac{\mu_{0}\pi a^{4}}{2l^{3}}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.