Generating Current in an Electric Field

I have a question:

Suppose I have a circuit with a resistor connected to a loop. The circuit is in an electric field. The loop has a 3 way switch that can close the loop regularly, or close the loop by connecting to wire that connects to a different part of the loop. My question is that if I switch the switch is an electric current generated through the wire?

I tried to draw it. The wires that aren't connected on the left is where the resistor goes.

emf = -dBflux / dt

dBflux / dt = integral(B . dA)

The field is constant, and I think area is changing, but intuition tells me a current shouldn't be generated.

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krab
You say "electric" field, but then give a formula that applies to magnetic field. So which is it?

My mistake. The entire circuit is in a magnetic field perpendiclar to the cicuit. Thank you for pointing that out. Do you have any ideas of whether or not a current is generated?

BMan said, "The field is constant, and I think area is changing, but intuition tells me a current shouldn't be generated."

Your intuition is correct! No current will flow. In cases like this it helps to think about the fundamental physics that causes the emf around a loop of wire. The cause is motion of the wire (which contains mobile charges) relative to a magnetic field. Aside from your switches (which can be igored) no wires are moving relative to the field. No relative motion => no emf.

That's what I thought. But then the current can also be caused by a change in the magnetic flux through the loop. (i.e. increasing or decreasing the strength of the magnet)

And also, the current can be caused by a change in the area of the loop, which can be thought of as moving free charges as you said, but I thought it could also be interpreted as appending the loop with more wire to increase the area.

Also, at the moment the magnetic field is "turned on", there is a current flow through the wire. The current is larger for the bigger loop, than the smaller loop (bigger and smaller loops, when they are switched to accordingly). V=IR, therefore the Voltage created by the change in magnetic field differs between the two possible paths.

Once the magnet is on and has been for a while, there is no current. There are a certain amount of electrons in the wire. If they are stable with the small loop path, and suddenly it is changed into the big loop path, will they not create a current to counter the "change" in magnetic field through the loop? (because the loop is bigger now) and adjust to the new path?

Big loop or small loop, it doesn't matter. The switching back and forth notion is a red herring. The real question is whether or not a current is generated in a stationary loop of wire in a magnetic field simple by closing the circuit of the loop.

Bman asked, "There are a certain amount of electrons in the wire. If they are stable with the small loop path, and suddenly it is changed into the big loop path, will they not create a current to counter the "change" in magnetic field through the loop? (because the loop is bigger now) and adjust to the new path?"

No, stick with your intuition! Magnetic fields don't exert forces on charges that are stationary with respect to the field.

Hmm. Well if a current is not generated, then there needs to be a disclaimer about Area in that formula. I thought for sure a change in Area would lead to a current.

Suppose the situation was somewhat reversed: The external magnetic field is removed. The circuit is connected to a battery, and then the switch is thrown. Wouldn't there be a change in magnetic field created by the current through the circuit?

And if yes, then why isn't the reverse possible?

BMan said:
Hmm. Well if a current is not generated, then there needs to be a disclaimer about Area in that formula. I thought for sure a change in Area would lead to a current.

Suppose the situation was somewhat reversed: The external magnetic field is removed. The circuit is connected to a battery, and then the switch is thrown. Wouldn't there be a change in magnetic field created by the current through the circuit?

And if yes, then why isn't the reverse possible?
To generate current there has to be relative motion between the conductor (loop) and the magnet. They can both be moving, or just one can be moving, but if neither is moving, there is no current generated. Switching the circuit from one loop to the other when neither is moving, is pointless.

jdavel explained this above:
jdavel said:
In cases like this it helps to think about the fundamental physics that causes the emf around a loop of wire. The cause is motion of the wire (which contains mobile charges) relative to a magnetic field. Aside from your switches (which can be igored) no wires are moving relative to the field. No relative motion => no emf.

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Forgot to include:

You can generate current in the coil if both are stationary, if you are constantly changing the strength or polarity of the magnetic field. If your magnetic field is created by an electromagnet you can a rig up a way for the strength of the current to be constantly changing, or so that the polarity of the electromagnet's field is constantly changing.

If you turn the electromagnet on and leave it that way, then it is no different than a permanent magnet and no current will be generated.

zoobyshoe said:
To generate current there has to be relative motion between the conductor (loop) and the magnet. They can both be moving, or just one can be moving, but if neither is moving, there is no current generated. Switching the circuit from one loop to the other when neither is moving, is pointless.

jdavel explained this above:

Relative motion between the loop and the magnet... but what about a generator? The net movement relative to the magnetic field is 0. Consider a 1/8th turn of the loop. Half of the loop went downfield, the other half went upfield. Net movement = 0.

Another example. If a loop is perpendicular to the field, you can move it around all you want and it will never generate a current.

You must consider the area of the loop and its orientation to the field in order to explain these phenomena.

Do straight wires moving in a magnetic field of uniform direction even create a net current? I'm pretty sure they do not. The field would have to be rotating in order to create a current on a straight wire.

BMan said:
Relative motion between the loop and the magnet... but what about a generator? The net movement relative to the magnetic field is 0.
What does "net movement" have to do with it?
Another example. If a loop is perpendicular to the field, you can move it around all you want and it will never generate a current.
This would be of note if anyone had said "All relative motion between a conductor and a magnet will generate current," which, of course, no one said.
You must consider the area of the loop and its orientation to the field in order to explain these phenomena.
True. I wasn't trying to explain all of the phenomena, just to point out that your set up lacks the bare esentials for generating a current.

Ok, this is what I'm saying: The "moving wire is the cause of current induced in a loop in a non-changing magnetic field" explanation that jdavel came up with can explain why my circuit will not create a current. But the explanation is not consistent with the generators and perpendicular loop examples.

If an explanation can disprove my circuit, but doesn't hold up against other examples that are known to work... it must not be the correct explanation.

I believe you when you say a current won't be generated in my circuit. I'm just looking for an answer to why. Playing the devil's advocate so I can find the true answer.

Also: With the generator, I say net movement because the current created by half of the movement cancels with the current created by the other half, according to jdavel's explanation.

Bman,

My explanation may not have been enough to explain how a generator works.

What you're calling motion "downfield" and "upfield" in a generator coil has nothing to do with creating the emf. It's motion of the wire ACROSS the field. One side of the loop, say the left, cuts in one direction forcing the charges, let's say, up. The right side cuts through the field in the other direction forcing charges down. But up on the left and down on the right are both clockwise. Thus, a current.

An even easier way (I think) to see how the generator produces voltage is to go back to your equations for the rate of change of flux. When the plane of the loop is perpendicular to the field, the flux is at a maximum. Then the loop rotates 90 degrees and becomes parallel to the field => no flux. And there's your voltage!

Ah! I see now. Ok ok. That is what I didn't understand. I forgot all about the across the field thing, I was thinking into and out of the field, like gravity. Ok, I am convinced then. So motion creates the current. No motion, no current. Thank you everyone. (I can be stubborn sometimes, but I'd rather understand than just accept)

I blame the change in flux equation for the misunderstanding. But I guess I can forgive it. =)