# Why is there current induced on Faraday's disk?

1. Apr 16, 2013

### raopeng

Because according to Faraday's law there should be a change in the flux to generate electric potential for a current to take place. But in that case no flux change happens. This can be reasonably explained by Lorentz force(charge separation due to radial Lorentz force) but can we still apply Faraday's law here? I feel it is because that since we must observe the current in a frame inert to the disk, so the magnetic field, under Lorentz transformation, is not constant anymore, hence the change in flux in that frame of reference.

2. Apr 16, 2013

### cabraham

Dr. Munley explained this. A search might turn up his paper. The electrons move radially due to Lorentz force. As the disk rotates, the circuit path traced is a pie sector shape. One terminal of the ammeter is on the center spindle, with the other terminal a peripheral contact, i.e. a brush type connection. As the electrons move they sweep out an area increasing with angle theta, which equals omega*t, where omega is angular speed.

The area of the filamentary circuit, times the constant flux density B, equals the flux phi. Although B is static, phi is time changing in proportion to time to the 1st power. Since emf = -d(phi)/dt, the emf is the 1st derivative of flux wrt time. But time is raised to the 1st power, so emf is a constant, nonvarying w/ time. Observation affirms this, that the induced emf/current is indeed dc.

Flux phi equals flux density B times area. If B varies we have induction. If B is static but area A varies, we have induction. A variation of phi wrt time is needed for induction to happen. The phi variation is usually due to B variation, i.e. area A is usually fixed in xfmrs, generators, motors, solenoids, etc. But a Faraday disk is a case where the reverse happens, fixed B, varying A. Since phi is the product of the 2, phi varies in time, hence induction occurs.

Did I help? I will clarify if needed.

Claude

3. Apr 16, 2013

### raopeng

Thank you so much. And that Dr. Munley's paper helps a lot too.