A conducting loop of area 5.0 cm2 is placed in a magnetic field which varies sinusoidally with time as B = B0 sin ωt where B0 = 0.20 T and ω = 300 s–1. The normal to the coil makes an angle of 60° with the field. Find

(a) the maximum emf induced in the coil,


(b) the emf induced at τ = (π/900) s and


(c) the emf induced at t = (π/600) s.



Given:


Area of conducting loop=


Variation of magnetic field with time


Angle of field with normal to coil θ =60°


Magnetic flux due to magnetic field B through cross section area A is given by



Here flux through the loop is given by


. (i)


Also,


by faraday’s law of electromagnetic induction



Where


ϵ =emf produced


ϕ =flux of magnetic field


using eqn.(i)


we get


…(ii)


Since maximum value of cosωt =1


Therefore, maximum value of magnitude of emf induced in the loop is given by



Putting the values of B0 and ω we get,



Therefore, maximum value of emf induced in the coil is 0.015V


(b) from eqn.(ii), we have



At t=π/900 s magnitude of induced emf is given by



Therefore magnitude of induced emf at t=π/900 is


(c) from eqn.(ii), we have



At t=π/600 s magnitude of induced emf is given by



Therefore magnitude of induced emf at t=π/600 is


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