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Induced EMF via changing magnetic flux + Faraday's law + Lenz's law

Physics (Year 12) - Electro-magnetism

Dev Lohar

Relevant laws for electromagnetic induction

The 2 laws which are relevant to understand electromagnetic induction are Faraday’s law and Lenz’s law.

Faraday’s law states that the magnitude of EMF induced is proportional to the negative rate of change of magnetic flux. This can relationship can be expressed mathematically as:

Lenz’s law states that an induced emf always gives rise to an induced current whose magnetic field will oppose the change in the original magnetic flux. For example, imagine the north end of a magnet moving left towards a loop, as seen in the diagram below. This means that the change in magnetic flux inside the loop is positive, hence there needs to be an ‘induced’ magnetic flux which needs to point in the opposite direction (i.e. to the right) to oppose this change in flux. Using the right hand grip rule, where the fingers point through the loop to the right, then the thumb points in an anticlockwise direction around the loop. Therefore, the direction of the induced current is anticlockwise.

If the same magnet (with the same orientation) moves to the right away from the loop, then the induced current will flow in the opposite direction (i.e. clockwise).

In general, Faraday’s law explains the magnitude of the induced EMF whereas Lenz’s law explains the direction of the induced current.

Change in magnetic flux

The above example changed the magnetic flux through the loop by moving the magnet in and out of the loop. But there are many other ways that the magnetic flux can be changed:

  • Changing the strength of the magnetic field, B

  • Changing the area of the coil through the magnetic field

  • Changing the orientation of the coil with respect to the magnetic field

Eddy currents

Eddy currents is essentially a fancy name given to multiple loops of current induced in a conductor by a changing magnetic field.

Eddy currents are important because they apply a force on the source of the external magnetic field and this force opposes the motion of the source. Eddy currents oppose the motion because the magnetic field created by the eddy currents oppose the original magnetic field, which in a way acts like how a pair of repelling magnets repel one another. This concept is better understood through practical and experiments, such as the classic example of dropping a magnet through a metallic tube. You can watch these experiments online.

Eddy currents are useful because as we learnt earlier, eddy currents oppose motion, so they can used to slow objects down. Such as brakes used to slow down trains or roller coasters.

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