Pl ans 

Figure shows a rectangular coil of width a and length b is rotating in a uniform magnetic field.

 

Induced emf E in the coil is given as,   E = -dφ/dt  , where φ is magnetic flux

 

magnetic flux = B•A = B (ab) cosθ  where B is magnetic flux density, A is area of coil that equals (a b)

and θ is the angle made by coil with magnetic field direction.

 

Hence emf E = - (d/dt )[ B (ab) cosθ ] = - (d/dt )[ B (ab) cos(ωt) ] = B (ab) ω sin(ωt)

 

current i = ( induced emf ) / ( Resistance of coil ) = { [ B (ab) ω ] / R } sin(ωt)

 

Peak value of emf = B (ab) ω

 

Peak value of current = { [ B (ab) ω ] / R }

 

 

Graph of emf as a function of t is shown in figure