Electromagnetic Induction in a disc

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SUMMARY

The discussion focuses on the principles of electromagnetic induction in a disc, specifically addressing the relationship between a time-dependent magnetic field and the resulting electric field and torque. The equation $$\frac{dΦ}{dt} = ε$$ is central to understanding the conversion of potential energy into rotational energy. The challenge lies in determining the time frame for switching off the magnetic field, which is stated to occur instantaneously, although a linear approximation over time T is suggested for calculations. The discussion emphasizes the role of angular momentum in deriving further insights.

PREREQUISITES
  • Understanding of electromagnetic induction principles
  • Familiarity with the equation $$\frac{dΦ}{dt} = ε$$
  • Knowledge of torque and angular momentum concepts
  • Basic grasp of energy conservation in physical systems
NEXT STEPS
  • Study the effects of time-dependent magnetic fields on electric fields
  • Explore the relationship between torque and angular momentum in rotating systems
  • Investigate energy conservation principles in electromagnetic systems
  • Learn about the mathematical modeling of instantaneous versus gradual changes in magnetic fields
USEFUL FOR

Students and educators in physics, particularly those focusing on electromagnetism, as well as engineers and researchers involved in applications of electromagnetic induction in mechanical systems.

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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