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