- #1

sudera

- 25

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- Homework Statement
- How does conservation of energy apply when placing an inductor next to another inductor with a current ##i(t) = at## going through it?

- Relevant Equations
- ##\varepsilon = -\dfrac{d\Phi_B}{dt}##

This is more like a theoretical question of my own than actual homework.

Say there is a circuit with a current source and an inductor. There is a current ##i(t)=at## going through the inductor. We now place a new circuit with an inductor and a resistor next to it. The current ##i(t)## causes a changing magnetic flux - and thus an emf - through this new circuit. Since ##i(t)## is linear, the emf is constant, and the current in the new circuit will also be constant and will not create a changing magnetic flux through the original circuit, so the current in the original circuit doesn't change. In other words, the second circuit received current and energy for free.

Obviously, this can't be true because of the law of conservation of energy. But where does this reasoning go wrong? I know there is a back emf in the transient state when the second inductor is introduced, but what happens in the steady state?

Say there is a circuit with a current source and an inductor. There is a current ##i(t)=at## going through the inductor. We now place a new circuit with an inductor and a resistor next to it. The current ##i(t)## causes a changing magnetic flux - and thus an emf - through this new circuit. Since ##i(t)## is linear, the emf is constant, and the current in the new circuit will also be constant and will not create a changing magnetic flux through the original circuit, so the current in the original circuit doesn't change. In other words, the second circuit received current and energy for free.

Obviously, this can't be true because of the law of conservation of energy. But where does this reasoning go wrong? I know there is a back emf in the transient state when the second inductor is introduced, but what happens in the steady state?