# The Faraday disc (unipolar generator) and Lenz' law

• Niles
In summary, the law states that the change in magnetic flux (as measured by an induced EMF) is proportional to the rate of change in magnetic field.

## Homework Statement

Hi all.

I can't seem to understand how to apply Lenz' law to a disc rotating in a magnetic field that is perpendicular to the discs plane (see first page on PDF):

http://www.pa.uky.edu/~latimer/phy232s08/lectures/phy232l31_4.pdf [Broken]

I can see that using the right-hand rule, positive charge will build up on the edge and negative at the center. So an EMF will run from the outer edge to the center, but I can't seem to relate this to Lenz' law. The change in magnetic flux will just get larger because of the induced EMF, and not opposed?

Last edited by a moderator:
Niles said:
I can see that using the right-hand rule, positive charge will build up on the edge and negative at the center. So an EMF will run from the outer edge to the center, but I can't seem to relate this to Lenz' law. The change in magnetic flux will just get larger because of the induced EMF, and not opposed?

If you've seen the analysis for "motional EMF" that is done for a conductive bar sliding on conductive rails in a uniform perpendicular magnetic field, you'll find this explanation is analogous.

For the rotating disc, imagine a specific radial line. Let's picture things so that you are facing one side of the disc with the magnetic field coming toward you, and the disc is rotating counter-clockwise. The imaginary radial line will be sweeping out a sector of a circle with area
(1/2)·(r^2)·(theta), where the angle theta is the angle through which the disc has rotated, starting from the moment you choose to be t = 0. You would use this to work out the rate of flux change for Faraday's Law, etc.

Now think of the boundary of this circular sector (shaped like a wedge). The amount of magnetic flux toward you is increasing in time. Using Lenz' "Law", we would argue that induced current must flow clockwise along the boundary of the sector so that magnetic flux away from you would be generated, in order to oppose the change in flux through the imaginary sector. On the side of the boundary where our imaginary radial line is, that induced current would flow from the center of the disc to the edge. So we find the charge separation described, as long as the disc keeps rotating.

This is consistent with the behavior expected by applying the magnetic force equation. A positive "charge carrier" is moving instantaneously on a tangent in the counter-clockwise direction in our view, with the magnetic field coming towards us. The cross product v x B then points radially away from the center of the disc.

Last edited:
Thank you for replying. A very precise description - good job!

## 1. What is a Faraday disc (unipolar generator)?

A Faraday disc, also known as a unipolar generator, is a device that converts mechanical energy into electrical energy through the principle of electromagnetic induction. It consists of a spinning disc with a series of conducting segments on its surface, which are connected to a central shaft. As the disc spins, the conducting segments cut through the magnetic field, producing an electric current.

## 2. How does a Faraday disc work?

A Faraday disc works through the interaction between a magnetic field and a moving conductor. When the disc spins, the conducting segments cut through the magnetic field, inducing a voltage in the segments. This voltage creates an electric current, which can be used to power electrical devices.

## 3. What is Lenz' law and how does it relate to the Faraday disc?

Lenz' law is a basic law of electromagnetism that states that the direction of an induced current is always such that it opposes the change that produced it. In the case of the Faraday disc, this means that the direction of the induced current is always opposite to the direction of the disc's rotation. This is due to the magnetic field generated by the disc, which opposes the change in the magnetic field caused by the disc's rotation.

## 4. What are the practical applications of the Faraday disc?

The Faraday disc has various practical applications, including power generation in hydroelectric dams, wind turbines, and steam turbines. It is also used in some forms of electric motors and generators, as well as in some scientific experiments and demonstrations.

## 5. Can the Faraday disc be used to produce unlimited amounts of energy?

No, the Faraday disc, like all generators, requires an external source of energy to produce electricity. It simply converts mechanical energy into electrical energy. Therefore, the amount of energy it can produce is limited by the amount of mechanical energy that can be input into the system.