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A square coil of 20 cm side and with 200 turns is rotated at a uniform velocity of 10 m/s about an axis at right angles to a uniform magnetic field having a flux density of 0.5 T. Determine the instantaneous value of the induced emf when the plane of the coil is in the plane of the field. 

A square coil of 20 cm side and with 200 turns is rotated at a uniform velocity of 10 m/s about an axis at right angles to a uniform magnetic field having a flux density of 0.5 T. Determine the instantaneous value of the induced emf when the plane of the coil is in the plane of the field.  Correct Answer 200 V

Concept:

EMF induced in a moving conductor. The emf induced in a straight conductor of length l moving with velocity v perpendicular to a magnetic field B is

E = Blv

Where B, l, and v are mutually perpendicular.

The emf is in volts

B is in webers/m2

l is in meters

v is in m/sec.

If the velocity vector v makes an angle θ with the direction of the magnetic field, then

E = Blv sin θ

EMF induced in the coil would be zero when its plane is at right angles to the plane of the field, even though it will have maximum flux linked with it. i.e. θ = 0°

However, the coil will have a maximum EMF induced in it when its plane lies parallel to the plane of the field even though it will have minimum flux linked with it. i.e. θ = 90°

Calculation:

Magnetic flux density (B) = 0.5 T, N = 200

Net effective length (L) = N × Length (l) = 200 × 200 cm = 40 m

Velocity (v) = 10 m/s

θ = 90°

E = BLv sin θ = 0.5 × 40 × 10 × sin 90°

E = 200 V

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