Faraday's and Lenz's Law - square coil

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SUMMARY

The discussion focuses on calculating the current (i) and angular frequency (ω) of a square coil rotating in a uniform magnetic field of B = 0.6T. The coil has a side length of a = 2cm and a resistance of R = 0.1 ohm. The total electromotive force (emf) is given by the equation emf = 0.2 + 0.24sin(ωt), where the induced emf is expressed as ε_i = Ba²ω sin(ωt). For the current to remain constant, the generator's emf and the induced emf must be out-of-phase, resulting in a net constant emf of 0.2V.

PREREQUISITES
  • Understanding of Faraday's Law of Electromagnetic Induction
  • Familiarity with the concept of electromotive force (emf)
  • Knowledge of Ohm's Law and its application in electrical circuits
  • Basic principles of alternating current (AC) and phase relationships
NEXT STEPS
  • Study the derivation of Faraday's Law and its applications in rotating coils
  • Learn about the relationship between emf, current, and resistance in electrical circuits
  • Explore the concept of phase difference in AC circuits and its impact on current flow
  • Investigate the effects of varying magnetic fields on induced emf and current
USEFUL FOR

Students studying electromagnetism, electrical engineers, and anyone interested in the principles of electromagnetic induction and circuit analysis.

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Homework Statement


A square coil rotates around an axis passing through the center. It is inside a magnetic field of B= 0.6T uniform and constant. The side of the coil is a = 2cm, the resistance R is 0.1 ohm.

The coil is powered by a generator that gives an emf = 0.2 + 0.24sin(ωt).
The current during the motion of the coil is constant. Calculate i and ω.

The Attempt at a Solution



The induced emf is \epsilon_i = Ba^2\omega sin(\omega t).

I can't understand how to go on with the problem. I cannot understand why the current stays constant if both the intial emf and the induced emf changes as sin(ωt).

Could you help me please?
Thank you
 
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the total emf is part from the generator (given) and part from being induced.
For the current to be constant, these need to add to a constant emf (ie, be 180 deg out-of-phase) 0.2V.
So, given its (ohmic) Resistance, what is I ?
 

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