Question

A small circular coil of radius 1 cm and number of turns 100 is placed inside a long solenoid of radius 5 cm and number of turns 8 per cm. The axis of the coil is parallel to the solenoid axis. Then, the coefficient of mutual inductance of the two coils is (in milli Henry)

• A. 0.032
• B. 0.064
• C. 0.016
• D. zero

Answer 1

Answer: (A)

0.032

Field inside solenoid = $B=\mu Ni$

N - number of turns per length in solenoid $=800/m$

Flux linking the smaller coil = $\lambda =100\times \pi r^{2}B=100\times \pi r^2\mu Ni$

mutual inductance = $M=\frac{\lambda }{i}=100\times \pi r^2\mu N=3.15mH$