(a) Dfine mutaul indutace and write its S.I. unit.
(b) A square loop of side 'a' carrying a current `I_(2)` is kept at distance x from an infinitely long straight wire carrying a current `I_(1)` as shown in thefigure. Obtain the expression for the resultant force on the loop.

Explanation

(a) Mutual Inductance : When current flowing in onr of the two nearby coils changed, the magnetic flux linked with the other coil changes, due to which an e.m.f. is induced in it other coil.

`phi=MI`
M is called coefficient of Mutual Inductance.
It's unit is Henry.
(b) Force of Repulsion on conductor AB due to EF
`F_(1)=mu_(0)/(4pi)(2I_(2)I_(2)a)/x`
Force of attraction on conductor CD due to EF
`F_(2)=mu_(0)/(4pi)(2I_(1)I_(2)a)/(x+a)`
Net force on the loop as `F_(1)gtF_(2)`
`F=F_(1)-F_(2)`
`F=(mu_(0)2I_(1)I_(2)a)/(4pi)[1/x-1/(x+a)]`
`F=(mu_(0)2I_(1)I_(2)a)/(4pi)[(x+a-x)/(x(x+a))]`
`F=(mu_(0))/(4pi)(2I_(2)I_(2)a^(2))/(x(x+a))`