Question

A small circular loop of radius a is placed inside a large square loop of edge `L(gt gta)` . The loops are coplanar and concentric. Find mutual inductance.

Answer 1

Magnetic field due to square loop at centre
`B_(1)=(mu_(0)i)/(4pird)(costheta_(1)+cos_(2))`
`=(mu_(0)i)/(4pi.(L)/(2))(cos45^(@)+cos45^(@))=(mu_(0)i)/(sqrt(2)piL`
`B_(0)=4B_(1)=(2sqrt(2)mu_(0)i)/(piL)`
Flux through smaller loop
`phi=B_(0)(pia^(2))=(2sqrt(2)mu_(0)ipia^(2))/(piL)=Mi`
`M=(2sqrt(2)mu_(0)a^(2))/(L)`