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Welcome to our Physics lesson on Lentz Law, this is the first lesson of our suite of physics lessons covering the topic of Lentz Law, you can find links to the other lessons within this tutorial and access additional physics learning resources below this lesson.
In the previous tutorial, we explained the Faraday's Law, which 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 the Lenz's Law .
It is not very common in Physics that a minus placed in the formula of a certain law (here Faraday's Law) produces another law (Lentz Law). This means the direction of the induced emf in a coil is very important. Faraday was aware of the direction, but Lenz stated it explicitly, so he is credited for its discovery.
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 Bi and it can be in the same or opposite direction of the original magnetic field produced by the moving magnet.
We can think this phenomenon similar to when we walk near a dog as mentioned in the beginning of this tutorial. If we assault the dog, it will rush against us but if we try to avoid the dog, the chance to be unharmed by the end of this situation increases.
The strategy used to solve problems involving the Lentz Law consists on the following steps:
Let's consider an example to make this point clear. If a magnet is moving towards a coil as shown in the figure,
a new magnetic field is generated because of the current induced in the coil as a result of magnet's motion. This induced magnetic field Bi opposes the magnet's motion and if considered the above figure, the direction if the induced magnetic field is as shown below:
Since an induced current is produced due to the magnet's motion relative to the coil, an emf is induced in the coil as well. Therefore, the magnetic flux in the coil changes based on the Faraday's Law:
If the magnet moves in the direction shown in the figure (towards the coil), the magnetic flux increases because more magnetic field lines enter the coil. This is obvious from geometry as when we move the magnet closer to the coil, the angle formed by the magnetic pole and the coil increases and as a result, more field lines enter the coil. As a result, the total magnetic field produced is
where B is the original magnetic field produced by the magnet and Bi is the induced magnetic field produced when the magnet moves towards the coil.
When the magnet moves in the opposite direction, the magnetic field of magnet is still in the original direction as the magnet only displaces horizontally; its poles does not change direction. However, an induced magnetic field in the opposite direction will be produced due to the induced current and emf of the coil. They also change direction to the previous case and thus, we obtain the setup shown in the figures below:
The magnetic flux in this 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.
A copper coil is placed inside a uniform magnetic field where the plane of coil is normal to the field lines. A copper ring slides downwards from position 1 to position 6 as shown in the figure. Determine the direction of the induced current (if any) for each position.
Now, we can discuss a numerical example to make clear this point (how to apply the Lentz Law).
A rectangular coil of area 0.4 m2 is placed inside a uniform magnetic field of magnitude B = 1.2 T. The coil rotates by 90° clockwise until it occupies a vertical position. This process takes 0.02 s. Calculate:
Using the right hand rule (when grasping the lateral sides of the coil, the four curled fingers show the induced magnetic field while the outstretched thumb shows the direction if the induced current) we find that the induced current flows through the resistor from right to left.
You have reached the end of Physics lesson 16.8.1 Lentz Law. There are 2 lessons in this physics tutorial covering Lentz Law, you can access all the lessons from this tutorial below.
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