4.5 - Electromagnetic Induction

Magnetic flux

If a single-turn coil of wire encloses an area A, and a magnetic field B makes an angle θ with the normal to the plane of the coil, the magnetic flux through the coil is given by Φ = AB cos θ.

Symbol for magnetic flux

Φ

Units for magnetic flux

Wb = Tm²

Flux linkage

If a coil consists of N turns, the flux linkage is given by NΦ

Symbol for flux linkage

NΦ

Units for flux linkage

Wb or Wb turn

Faraday’s law

When the flux linking an electrical circuit is changing, an emf is induced in the circuit of magnitude equal to the rate of change of flux linkage

E = − ∆(NΦ)/∆t

Lenz’s law

The direction of any current resulting from an induced emf is such as to oppose the change in flux linkage that is causing the current.

Fleming’s Right Hand Rule

Find the direction of the induced current

How to calculate induced emf

Calculate flux linkage at t=0 and flux linkage at t=t

Subtract one from the other

Divide by t

• This gives the average emf induced over that time

2 ways to induce an emf

1. Changing area over time

2. Changing flux density over time

How to induce an emf by changing area over time

• Increase area of loop —> flux linkage increases

• Substitute area into equation for Faraday’s law

• Calculate emf

How to induce an emf by changing flux density over time

• Substitute into Faraday’s law

• Divide by t

How induce an emf using a generator

Rotating coil in a magnetic field

Factors that affect instantaenous emf

• Flux density

• Area of coil

• Angular velocity

• Position of the coil

Explain how flux density affects instantaneous emf

• Larger flux density

• Larger flux linkage

• In a given time, change in flux density would be larger

• Induced emf would be greater

Explain how area of the coil affects instantaneous emf

• Larger area

• Larger flux linkage

• Induced emf would be larger

Explain how angular velocity affects instantaneous emf

Larger angular velocity means the change in flux linkage would happen is a smaller time. Therefore, the induced emf would be larger but the frequency of the emf would also be larger.

Explain how the position of the coil affects instantaneous emf

• At position A, the coil is vertical, therefore θ = 0° and cosθ = 1. The flux linkage is a maximum at that point; therefore, the rate of change of flux linkage is at its minimum. Emf = 0

• At position B, the coil is vertical, therefore θ = 90° and cosθ = 0. The flux linkage is 0 at that point; therefore, the rate of change of flux linkage is at its maximum.