# Lenz's Law in DC Motors and Magnetic Braking

This is part of the HSC Physics course under the topic Electromagnetic Induction.

### HSC Physics Syllabus

• relate Lenz's Law to the law of conservation of energy and apply the law of conservation of energy to:
- DC motors and
- magnetic braking

### Lenz's Law and Electromagnetic Braking

This video applies the law of conservation of energy to magnetic braking. Lenz's Law and DC motors was explored earlier through the discussion of back emf.

### What Is Electromagnetic Braking?

Electromagnetic braking is the use of magnets to bring a system to rest. When an object moves through a magnetic field, the change in flux causes it to experience an induced emf by Faraday's law. In the example below, where a wheel rotates through a magnetic field, this induced emf creates eddy currents.

The magnetic field associated with the eddy currents will act to oppose the initial change in flux, by Lenz's law. For example, in the section of the wheel moving into the magnetic field, the eddy currents will be anti-clockwise as viewed from above. This creates a magnetic field that repels the wheel backwards, away from the magnet. Simultaneously, the part of the wheel moving out the magnet experiences a decrease in flux. The eddy current here will be clockwise, producing a magnetic field that attracts the wheel backwards.

Both eddy currents thus develop a torque anti-clockwise, against the rotation of the wheel. This slows the wheel down.

This principle of magnetic braking is used to bring cars to rest. When the car brake is off, the electromagnets near the wheels are turned off. This means that there will be no external magnetic field to magnetically brake the wheels.

There are many advantages to magnetic braking. For example, there is no friction involved, and this allows car wheels to require less maintenance. The magnitude of resisting force increases with the magnitude of induced current, which increases the speed of rotation. As such, faster cars can be brought to stop more effectively.

### Electromagnetic Braking and Law of Conservation of Energy

Electromagnetic braking can be analysed in terms of the law of conservation of energy. Any moving body has kinetic energy, and this is converted into electrical energy (the current produced).

The electrical energy is then lost as heat through resistive heating.

Practice Question 1

(a) All transformers which operate using the principle of Faraday’s electromagnetic induction have less than 100% efficiency. Explain why this is the case. (4 marks)

(b) Explain one strategy that is used to overcome the problem(s) you outlined in (a). (2 marks)

Practice Question 2

The primary coil of a transformer has 4800 turns and is supplied by 240 V AC. The secondary circuit operates a small electric motor of resistance 192 ohms which requires 0.5 A.

(a) Calculate how many turns the secondary coil should have.

(b) The current flowing in the primary circuit is 0.21 A. Calculate the efficiency of the transformer.

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