EMF Induced in a Rotating Coil in a Uniform Magnetic Field

The emf induced in a coil rotating with a uniform angular velocity in a uniform magnetic field is given by Faraday's law of electromagnetic induction. This law states that an emf is induced in a circuit whenever the magnetic flux through the circuit changes.

Formula for EMF Induced

The formula for emf induced in a rotating coil in a uniform magnetic field is:

E = (-NΦBωsinθ)

Where,
E = emf induced (in volts)
N = number of turns in the coil
Φ = magnetic flux through the coil (in webers)
B = magnetic field strength (in teslas)
ω = angular velocity (in radians per second)
θ = angle between the plane of the coil and the magnetic field.

Explanation of the Formula

The emf induced in a coil rotating in a uniform magnetic field is due to the change in magnetic flux through the coil. The magnetic flux through the coil is given by:

Φ = BANcosθ

Where,
A = area of the coil (in square meters)
N = number of turns in the coil
B = magnetic field strength (in teslas)
θ = angle between the plane of the coil and the magnetic field.

When the coil rotates with an angular velocity ω, the angle θ between the plane of the coil and the magnetic field changes, causing a change in magnetic flux through the coil. The rate of change of magnetic flux through the coil is given by:

dΦ/dt = BANωsinθ

Therefore, the emf induced in the coil is given by:

E = -dΦ/dt = (-NΦBωsinθ)

Applications of the Formula

The formula for emf induced in a rotating coil in a uniform magnetic field has several applications in electrical engineering, including:

1. Electric generators: In electric generators, a rotating coil is used to generate electrical energy from mechanical energy. The formula for emf induced is used to calculate the output voltage of the generator.

2. Electric motors: In electric motors, a rotating magnetic field is used to generate mechanical energy from electrical energy. The formula for emf induced is used to calculate the torque produced by the motor.

3. Induction heating: In induction heating, a high-frequency alternating current is passed through a coil to generate a magnetic field, which induces eddy currents in a metal object placed inside the coil. The formula for emf induced is used to calculate the power dissipated by the eddy currents.

Conclusion

The emf induced in a coil rotating in a uniform magnetic field is given by the formula E = (-NΦBωsinθ). This formula is used in various applications in electrical engineering, including electric generators, electric motors, and induction heating.