Lentz Law Revision Notes

In these revision notes for Lentz Law, we cover the following key points:

• What is the definition of Lentz Law? What do we find using it?
• How the Lentz Law is related to the Faraday's Law of Induction?
• What strategy do we use to solve problems involving the implementation of Lentz Law?
• What is the induced magnetic field? When does it appear?
• What happens to the magnetic flux when a magnet moves towards to or away from a coil?

Lentz Law Revision Notes

The Faraday's Law expresses the induced emf as a rate of flux change. The mathematical expression of Faraday's Law is

The minus sign in Faraday's law of induction is very important. The negative sign means that the induced emf creates a current (induced current) and magnetic field (induced magnetic field) that oppose the change in flux. This statement is known as Lenz's Law.

When we move a magnet towards to or away from a coil, we must consider two magnetic fields: one is the magnetic field B possessed by the magnet and the other is a new magnetic field produced in the coil due to the presence of the induced current. This new magnetic field is known as the induced magnetic field B_i and it can be in the same or opposite direction of the original magnetic field produced by the moving magnet.

The strategy used to solve problems involving the Lentz Law consists on the following steps:

1. Making a sketch that helps is a better understanding of situation through visualization.
2. Determining the direction of the magnetic field B.
3. Determining whether the flux is increasing or decreasing.
4. Determining the direction of the induced magnetic field B_i. It is either added to or subtracted from the original field. However, one thing is sure: it always opposes the motion.
5. Using the Right Hand Rule to determine the direction of the induced current that is responsible for the induced magnetic field B_i.
6. The direction (or polarity) of the induced emf will now drive a current in this direction and can be thought as current emerging from the positive terminal of the emf and returning to its negative terminal.

The total magnetic field produced therefore is

where both fields are in the same direction and

when they are in opposite direction. The magnetic flux in the second case decreases with time as less magnetic field produced by the mar magnet enter the coil. As a result, an induced emf (and therefore an induced current) will appear in the coil based on the Faraday's Law. This induced current is in the opposite direction to before.

The increasing flux when the magnet approaches the loop is opposed by the north pole of the magnetic dipole directed upwards. From the curled right hand rule we can find the direction of the induced current.

When the magnet moves away from the coil, the induced current changes direction as the magnetic dipole has its south pole directed upwards.

When the magnet is at rest, there is no flux change. Therefore, no induced current is produced in the loop. This means no induced magnetic field exists inside and around the coil. When the magnet is moved towards the coil (the N-pole of magnet approaching the coil), the flux increases. This brings the induction of an opposite magnetic field B_i.