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Question
Obtain the expression for the emf induced in the rotating coil of N turns each of cross-sectional area A, in the presence of a magnetic field `vecB` .
Solution
As the armature coil is rotated in the magnetic field, the angle θ between the field and normal to the coil changes continuously. Therefore, magnetic flux linked with the coil changes. An emf is induced in the coil. According to Fleming’s right-hand rule, current induced in AB is from A to B and it is from C to D in CD. In the external circuit, current flows from B2 to B1.
To calculate the magnitude of emf induced:
Suppose
A → Area of each turn of the coil
N → Number of turns in the coil
`vecB`→ Strength of magnetic field
θ → Angle which normal to the coil makes with `vecB` at any instant t
∴ Magnetic flux linked with the coil in this position:
`phi=N(vecB.vecA)=NBA cos theta=NBA cos omega t` .....(I)
Where ‘ω’ is the angular velocity of the coil
As the coil rotates, angle θ changes. Therefore, magnetic flux Φ linked with the coil changes, and hence, an emf is induced in the coil. At this instant t, if e is the emf induced in the coil, then
`e=-(d theta)/dt=-d/dt(NAB cos omega t)`
`=-NAB d/dt(cos omega t)`
`=-NAB(-sin omega t)omega`
`therefore = NAB omega sin omegat`
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