Obtain an expression for the emf induced in a coil rotating in uniform magnetic
filed ?
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Explanation:
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
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