Transformers: Uniform magnetic filed in relation to current flow

[dba]

Homework Statement

In our lab about transformers we have a question as follows:
Consider a loop in a uniform magnetic field. If the field is suddenly turned off, in which direction will the current flow in the wire?

Homework Equations

The Attempt at a Solution

My first thought was that if there is no current then there is no magnetic field but I am not sure. Thanks for any hint.

 

[gneill]

Currents are induced by the loop experiencing changes in the magnetic field, and in particular, changes in the magnetic flux within the area circumscribed by the loop.

Look up Faraday's law and Lenz's Law.

You will have to determine the direction of the change in flux that takes place when the field is switched off, and then determine the resulting direction of the induced current.

 

[dba]

Can you explain a little better what you mean by the direction of the change in the flux? For the problem, there are no numbers. There is a vertical loop and the direction of the field is to the right. The flux is the integral of B*A since B and da are parallel and A is pi*r^2. Thanks!.

 

[gneill]

The flux is the integral of B*da, and in this case since B starts out at some constant value, and since A is also constant, the flux is B*A.

If you were to represent the original flux as a vector pointing through the loop plane, it would be pointing in the direction of the magnetic field B (to the right, since that's the direction that you said that B points). What happens when the whatever is supplying B field is switched off? The B field collapses to zero, right? What then will be the direction of the change in flux?

 

[dba]

That is exactly what I do not understand. I do not know how to imagine a direction of a change. As I mentioned in the beginning, I would assume if my B goes to zero, then the flus will be zero and the current will be zero. therefore there would't be a direction.

 

[gneill]

That is exactly what I do not understand. I do not know how to imagine a direction of a change. As I mentioned in the beginning, I would assume if my B goes to zero, then the flus will be zero and the current will be zero. therefore there would't be a direction.

Often the interesting stuff happens while things are changing, not after they've changed

Before the field's disappearance the flux is B*A and is comprised of magnetic field lines of B, which have a definite orientation while passing through the plane of the loop. So when the field collapses, it's as though you're adding a counter-flux to oppose and cancel the flux of the B field. That is to say, the flux change is in the direction opposite that of B. The magnitude of that flux change is B*A if the field goes to zero.