# Transient current in inductance circuit

1. Aug 19, 2010

### krindik

1. The problem statement, all variables and given/known data

I have posted my complete question http://imagebin.org/110458" [Broken] [PLAIN]http://imagebin.org/110458. [Broken] It is about a DC circuit with an inductor and a static magnetic field applied on a part of the circuit loop. An expression for the transient current needs to be found. My attempt is below. But I have doubt whether an EMF is created in the wire, where there is magnetic field.

2. The attempt at a solution

There is no energy conversion from the mechanical system to the electrical system. Also, the steady magnetic field does not effect the current but only creates a force. (an opposing current will be induced only if the magnetic field changes, AFAIK). So, we can consider the electrical and mechanical systems separately,

considering the electrical system,
the voltage drop is only across the inductance
$$V = - L \frac{di}{dt}$$
so, $$i = -Vt/L$$
However, I'm in doubt whether there is a voltage drop across the wire which is created as an opposing EMF due to the changing current, even though the magnetic field is fixed.
This is where I'm not sure about my attempt.

considering the mechanical system
$$\tau = (i \times B)R = iBR = I \frac{d\omega}{dt}$$
=> $$\omega$$ = integration of above

Also, we should be able to verify this by considering energy conservation
energy given by battery (Vi) - energy stored in the inductor (Li di/dt) - momentum gained by the wheel (Iw) + work done by the magnetic field (torque times integration of omega with time) = 0

Can somebody point me in the correct direction?

Thanks.

rgds,
K

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