Question

Mutual inductance M between two concentric coils of radii 1 m and 2 m is

• A. $\frac{{\mu }_0\pi }{2}$
• B. $\frac{{\mu }_0\pi }{4}$
• C. $\frac{{\mu }_0\pi }{8}$
• D. $\frac{{\mu }_0\pi }{10}$

Answer 1

Answer: (B)

$\frac{{\mu }_0\pi }{4}$

Magnetic field inside the smaller coil due to large coil is uniform and equal to $\frac{{\mu }_{0}i}{2R_{large}}$

Thus, flux through the smaller coil due to this magnetic field $=\frac{{\mu }_{0}i}{2R_{large}}\pi R_{small}^2$

Thus, $M=\frac{\varphi }{i}=\frac{{\mu }_0}{2\times 2}\pi (1{)}^2=\frac{{\mu }_0\pi }{4}$