A circular conducting coil of radius 1 m is being heated by the change of magnetic field `vec(B)` passing perpendicular to the plane in which the coil is laid.
The resistance of the coil is `2mu Omega` The magnetic field is slowly switched off such that its magnitude changes in time as
`B=(4)/(pi)xx10^(-3)T(1-(t)/(100))`
The energy dissipated by the coil before the magnetic field is switched off completely is E = ____________ mJ.

Answer

80

Explanation

`phi=B.A=(4xx10^(-3))/pi.(1-t/100).pi.1^2`
`= 4 xx10^(-3)(1-t/100)`
`epsilon=|(dphi)/(dt)|=40xx10^(-6)`
`i=epsilon/R=(40 xx10^(-6))/(2xx10^(-6))=20A`
`E=i^2 R .t = 20^(2) xx 2 xx10^(-6)xx100`
`= 80 xx10^(-3) J`