Faraday's and Lenz's Law - square coil

AI Thread Summary
A square coil is rotating in a uniform magnetic field of 0.6T, with a side length of 2cm and a resistance of 0.1 ohm. The coil is powered by a generator providing an emf of 0.2 + 0.24sin(ωt), leading to a question about the constancy of current despite the varying induced emf. The induced emf is expressed as ε_i = Ba^2ω sin(ωt), and for the current to remain constant, the total emf from the generator and the induced emf must combine to a constant value. This requires the two emfs to be 180 degrees out-of-phase, resulting in a total emf of 0.2V. Understanding this phase relationship is crucial for calculating the current and angular frequency.
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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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