A metal disc of radius R rotates with angular velocity Omega (w) In a uniform magnetic field. Calculate the induced emf develop.
I am assuming the surface of the disk is perpendicular to the magnetic field. https://www.jiskha.com/display.cgi?id=1472983008
To calculate the induced electromotive force (emf) developed in the rotating metal disc in a uniform magnetic field, you can use Faraday's law of electromagnetic induction. According to Faraday's law, the induced emf is given by:
emf = -N * (dΦ/dt)
Where:
emf is the induced electromotive force,
N is the number of turns in the metal disc,
dΦ/dt is the rate of change of magnetic flux through the disc.
To calculate the rate of change of magnetic flux, you need to know the magnetic field and the area of the disc.
The magnetic field is assumed to be uniform, so the magnetic flux Φ through the disc is given by:
Φ = B * A
Where:
B is the magnetic field,
A is the area of the disc.
Since the metal disc is rotating, the area of the disc changes over time. The area of the disc can be given by:
A = π * R^2
Where:
R is the radius of the disc.
Now, to calculate the induced emf, you need to take the derivative of the flux with respect to time:
dΦ/dt = d(B * A)/dt
= B * dA/dt
= B * (2πR * dR/dt)
Finally, substituting this value back into Faraday's law, you get:
emf = -N * (dΦ/dt)
= -N * B * (2πR * dR/dt)
Therefore, the induced emf developed in the rotating metal disc is given by the equation: emf = -N * B * (2πR * dR/dt).