Lenz’s Law, DC Motors and Magnetic Braking – Learn


Essentially, Lenz’s Law is a consequence of the Law of Conservation of Energy, in part – energy can not be created or destroyed. Thus consider Lenz’s Law: An induced emf always gives rise to a current that creates a magnetic field that opposes the original change in flux through the circuit:

The emf is induced because there is a changing flux. The induced emf that is produced as a result of the changing external magnetic field, is in the opposite direction to the input voltage or supply emf. If this was not the case, the current would continue to increase, which would again increase the field, again increasing the current, and so on infinitely – this is clearly impossible. An induced emf produced by the relative movement of a conductor is known as the back emf because it is in the opposite direction to the supply emf.

Relating Lenz’s Law and the Law of Conservation of Energy can help us better understand:

  • DC motors, and
  • magnetic braking

Be sure to watch the YouTube clips in this section to better develop your conceptual understanding of these ideas.


Back emf in DC Motors

An analysis of the construction and operation of a DC motor and a generator illustrate that they have a lot in common. In fact, every motor can also be used as a generator. There are several examples where this occurs – motors of electric trains, for instance, work as generators when a train is slowing down, converting kinetic energy to electrical energy and putting it back into the electrical supply grid.

A DC motor will also generate an emf when running normally. This is termed the ‘back emf’. The back emf generated in a DC motor is the result of an induced current produced in response to the rotation of the rotor inside the motor in the presence of an external magnetic field. The back emf, following Lenz’s law, opposes the change in magnetic flux that created it, so this induced emf will be in the opposite direction to the emf creating it. The net emf used by the motor is thus always less than the supplied voltage:

{ \varepsilon }_{ net }\: =\: V\: -\: { \varepsilon }_{ back }

As the motor increases speed, the current induced in it will increase and the back emf will also increase. When a load is applied to the motor, the speed will generally reduce. This will reduce the back emf and increase the current in the motor. If the load brings the motor to a sudden stop, the current may be high enough to burn out the motor and the motor coil. To protect the motor, a resistor is placed in series. It is switched out of the circuit when the current drops below a predetermined level and is switched back into the circuit for protection once the level is exceeded.


Magnetic Braking

Conventional braking systems in cars and bicycles utilise the friction force between two objects pressed together to slow an object down. By making use of eddy currents, magnetic braking can be achieved where the electromagnetic force between a magnet and a conductor in motion is used to create a repulsive and slowing force. If a conductor moves past a stationary magnet, eddy currents will be induced in the conductor by the magnet, according to Faraday’s law of induction.

Eddy currents create their own magnetic field that opposes the original magnetic field of the magnet. This in turn creates a drag force between the magnet and the conductor, which slows the conductor down. A permanent magnet or an electromagnet can be used to create the magnetic field in a magnetic brake. The advantage of using an electromagnet is that the magnet, and hence the braking system, can be turned on and off by adjusting the current in the electromagnet’s windings.

A big advantage with magnetic braking is the lack of physical contact between components, which makes for low maintenance and few replacement parts. A disadvantage with magnetic braking is that when there is no motion between the magnet and conductor, there is no static force to maintain the conductor at rest. In this case, the magnetic braking system would need to be supplemented by a friction­ based (conventional) braking system like a hand brake.


Example:

An electric motor has a resistance of 8 Ω and is connected to a 240 V supply. The back emf is equal to 228 V when the motor is operating with a normal load.

a) What is the current that passes through the motor when it is first started?

b) What is the current that passes through the motor when it is operating normally?

Answers:

a) using: V=IR

I=\cfrac { V }{ R }

I=\cfrac { 240 }{ 8 }

I=30A\:

b) using: { \varepsilon }_{ net }\: =\: V\: -\: { \varepsilon }_{ back }

\varepsilon=240-228

\varepsilon =12\:V

V=IR

I=\cfrac { V }{ R }

I=\cfrac { 12 }{ 8 }

I=1.5A\:

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