Electromagnetic Induction in a disc

AI Thread Summary
The discussion centers on the principles of electromagnetic induction in a disc, focusing on the relationship between potential energy, rotational energy, and the effects of a time-dependent magnetic field. Participants explore how switching off the external magnetic field releases energy, which is linked to the torque generated by the induced electric field. The challenge lies in determining the timing of the magnetic field's shutdown, which is described as instantaneous, although a linear approximation over time T is suggested for calculations. The conversation emphasizes the conservation of energy and angular momentum in solving the problem. Overall, the key takeaway is the interplay between magnetic fields and induced electric fields in generating torque and energy transformations.
Yashbhatt
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Homework Statement


Please see the attached file.

Homework Equations


$$\frac{dΦ}{dt} = ε$$

The Attempt at a Solution


The only way I see is to apply some conservation of energy. But I don't know how. The potential energy is being converted to rotational energy. But how do I find the potential energy?
 

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Switching off the external field releases energy you cannot control here.

A time-dependent magnetic field leads to an electric field, which then leads to a torque. Angular momentum allows to calculate everything else then.
 
mfb said:
Switching off the external field releases energy you cannot control here.

A time-dependent magnetic field leads to an electric field, which then leads to a torque. Angular momentum allows to calculate everything else then.

The only problem I face here is I don't know in what time is the magnetic field switched off. It says it is switched off instantaneously.
 
It doesn't matter, a faster switching gives a larger torque for a shorter timescale. For calculations, you can assume that it gets switched off linearly during time T. This parameter (and also the assumption of linearity) will drop out of the calculations later.
 
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