Question

derive an expression for the emf induced in a coil due to change of area of the coil inside a magnetic field.​

Answer 1

Consider a coil of cross section area S rotating with an angular speed ω in a uniform magnetic field B as shown in the figure.

Magnetic flux through the loop in the given position is given by:
ϕ=
B
⋅
S

=BScos(π/2−θ)
=BSsin(θ)
θ=θ
o
​
+ωt
⟹ϕ=BSsin(θ
o
​
+ωt)

Induced emf is given by:
ε=
dt
dϕ
​

ε=
dt
d(BSsin(θ
o
​
+ωt))
​

ε=BSωcos(θ
o
​
+ωt)

Note that the induced emf is alternating in nature.
The rms value of induced emf is: ε
rms
​
=
2
​

BSω
​