# Lenz's Law applied to a non-circuit conductor?

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1. Dec 17, 2015

### kostoglotov

I was reading through my College Physics text, and it talked about how NASA once swung a 20km long conductor through the Earth's magnetic field and setup a 3500V potential difference along the wire.

I understand that there's no conventional current in that wire, it's not a circuit. But for a brief moment, in the instants that the charge was separating, wouldn't this momentary movement of charge behave briefly like a current? And if so, wouldn't that momentarily setup it's own magnetic field? Would Lenz's law about the direction of the current somehow conform to what was happening during the separation of charge here? (the momentarily induced magnetic field would simultaneously oppose, add to, be orthogonal to, etc the Earth's field) Does Lenz's law only apply to circuit with an effective area experiencing a changing magnetic flux?

Presumably work was done by the shuttle to achieve separation of the charge in the wire. Was no net power dissipated by the (briefly) induced magnetic field?

2. Dec 18, 2015

### MisterX

Lenz's law does not apply here because there is not a changing B field. There is no natural B-flux to even consider in this problem. The voltage produced in the wire is due to the magentic (Lorentz) force separating the charges in the the wire. This does cause a current momentarily. You can imagine that the circuit actually is closed and that the ends of the wire form a capacitor. So as the wire is dragged through the magnetic field, the ends of the wire will build up a charge difference until an equilibrium is reached between the static charge forces and the magnetic forces.

If you consider the geometry, you should find that in fact as current moves along the wire, on one side of the wire, the magnetic field will be enhanced, and the other side it will be weakened. It seems to me that it happens that he side of the wire in the direction the wire is moving will have a positive change in the B along the relevant direction, and the other side of the wire will have less B in that direction.

The energy required for the separation of charges was taken from the kinetic energy of the satellites. And yes, the momentary currents would radiate some power electromagnetically.