Question

A circular coil of radius r and number of turns n is placed at the centre of a big circular coil of radius R and number of turns N. Both the coils are coplanar. If R >> r, and M is the conductance of the pair of coils then M is proportional to

• A. nNr/R
• B. nNr${}^2$/R
• C. nNr${}^2$/R${}^2$
• D. nr${}^2$/NR${}^2$

Answer 1

Answer: (B)

nNr${}^2$/R

Magnetic field at the center of outer circular coil= $B=\frac{\mu Ni}{R}$

flux linking smaller circular coil = $\lambda =Bn\pi r^2=\frac{\mu Nin\pi r^2}{R}$

mutual inductance = $M=\frac{\lambda }{i}=\frac{\mu Nn\pi r^2}{R}$