A circular conducting coil of radius a and resistance R is placed with its plane perpendicular to a magnetic field. The magnetic field varies with time according to the equation `B=B_(0)sinomegat`. Obtain the expression for the induced current in the coil.

Explanation

As we know, induced current,
`I=("induced emf(e)")/("resistance (R)")`
Again, `e=-(dphi)/(dt)` = rate of change of magnetic flux with time
`therefore I=((-dphi)/(dt))/(R)=-(1)/(R).(d)/(dt)(BAcos0^(@))`
or, `I=-(A)/(R).(d)/(dt)(B_(0)sinomegat)[because B=B_(0)sinomegat]`
`=-(AomegaB_(0))/(R)cosomegat=-(pia^(2)omegaB_(0))/(R)cosomegat`