Square wire loop moving in a static B field.

[Robsta]

Homework Statement

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3. A square loop of area a 2 is formed from a single turn of thin wire of resistance R. The loop is aligned with two sides parallel to an infinite straight thin cable, with its closest side a distance r away, and is given a velocity v in a direction perpendicular to the cable. The cable, loop and direction of motion all lie in the same plane. A current I flows in the cable. Calculate the magnitude of the current induced in the loop.

Homework Equations

I've used a couple of Maxwell's equations and also the Lorentz force law and all lead me towards thinking that no current can be induced. This is wrong.

The Attempt at a Solution

The curl of E for example is the negative time derivative of the B field. Since the B field is static, E has no curl, so the line integral of E around the loop is zero, so there can be no current.

Alternatively from the Lorentz force law, the force on the charges in the two wires perpendicular to the cable will be the same. From symmetry they will cancel out. Thus no current.

Am I using maxwell's equations wrongly? Am I using the Lorentz force equation wrongly?

It seems to me there's no change of magnetic flux through the loop since the b field is constant at a given distance r from the cable.

 

[Robsta]

Gah! I've just realized that the wire moves PERPENDICULARLY to the wire. I thought it was moving parallel. This means the magnetic field does change and thankfully a current is induced. All solved

 

[theodoros.mihos]

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