As shown in the figure, a long wire is placed near a triangular coil. Calculate the mutual induectance of the combination.

Explanation

Area of strip `dA=b'dx`
`(h)/(b)=(x)/(b')` implies `b'=(b)/(h)x`
Magnetic field due to long wire at distance `(a+x)`
`B=(mu_(0)i)/(2pi(a+x))`
`dphi=BdA=(mu_(0)i)/(2pi)(b)/(h)(xdx)/((a+x))`
`=(mu_(0)ib)/(2pih)((a+xx-a)dx)/((a+x))`
`phi=(mu_(0)ib)/(2pih)int_(0)^(h)(1-(a)/(a+x))dx`
`=(mu_(0)ib)/(2pih)|x-a1n(a+x)|_(0)^(h)`
`=(mu_(0)ib)/(2pih){h-a1n(1+(h)/(a))}=Mi`
`M=(mu_(0)ib)/(2pih)[h-a1n(1+(h)/(a))]`