# A rectangular coil of n turns and area of cross section A , is held in a time varying magnetic field given by B=Bo sin wt , with the plane of the coil normal to the magnetic field . Deduce an expression for the emf induced in the coil .

54 Points
4 years ago
In this given question magnetic field(B) is variable.
Whereas, area(A) & angle ($\theta$) are constant.

$\Phi$ = BAcos($\theta$)

$\frac{d\Phi }{dt}$=$\frac{dB}{dt}$*Acos($\theta$)

= (w) Bo (-)sin(wt) A cos($\theta$)

Emf = – $\frac{d\Phi }{dt}$

Emf = (w) Bo sin(wt) A cos($\theta$)
= Bo A (w) cos($\theta$) sin(wt)