Exposing a coil or loop to a changing magnetic flux will generate a current if the circuit is complete. The direction of the current is given by Lenz's Law:

Lenz's Law: A changing magnetic flux induces an emf that produces a current which sets up a magnetic field that tends to oppose the change in flux.

Coils and loops don't like to change, and they will try to counteract any changes in magnetic flux imposed on them. They are not successful - the change can be made, but the coil or loop tries to oppose the change while the change is taking place.

This tendency to oppose is why there is a minus sign in Faraday's Law.

First, you'll need to remember that a clockwise current generates a field into the page inside the loop. A counter-clockwise current generates a field out of the page inside the loop.

To help explain the description below take the example of a loop in the plane of the page with a uniform magnetic field directed into the page. Over some time interval the field is doubled. What direction is the induced current in the loop while the field is changing?

An easy way to answer such a question is to draw three pictures:

1. Before: Draw the field lines in the loop before the the change takes place.
2. After: Draw the field lines in the loop after the change takes place.
3. To Oppose: Draw the loop with field lines such that when the After and To Oppose pictures are superimposed the result is the Before picture.

Once you've drawn the To Oppose picture, determine the direction of the current around the loop needed to produce field in that direction. That's the direction of the induced current.

Expressed as an equation, Before = After + To Oppose.

This corresponds to the opposing nature of Lenz's Law. The loop will do whatever it can to maintain the status quo (i.e., it will work to prevent the change).

This pictorial approach works well for determining the direction of the induced current. One problem with it, however, is that it can lead you to believe that the loop is successful at completely cancelling any change imposed on it. This is not the case. The loop fights the change, but it loses the fight in the end and the flux is eventually changed to that shown in the After picture.

A loop of wire has an area of 0.5 m² and a resistance of R = 0.1 W. There is a uniform magnetic field of B = 1.0 T passing through the loop into the page. The magnetic field is reduced steadily from 1.0 T to 0 over a 10 second period.
In other words DB/Dt = -0.1 T/s for 10 seconds.

Plot the magnetic flux as a function of time. Plot the induced current as a function of time.

What current is induced in the wire while the field is being reduced? Is the current clockwise or counter-clockwise?

To find current first find the induced emf:

e

=

– N

DFB Dt

=

– N

D (BA cosq) Dt

In this situation N = 1, and A and q are constants. This gives:

e

=

– A cos(q)

DB Dt

=

-0.5 x 1 x -0.1

=

0.05 V

The sign doesn't really matter here.

While the magnetic field is changing the loop acts as if it has a battery in it. Using Ohm's Law, the current is:

I

=

e R

=

0.05 0.1

=

0.5 A

The change reduces the number of field lines passing through the loop into the page. The field generated by the induced current must be into the page to oppose the change. That requires a clockwise current.

Let's return to our example and say that instead of reducing the the field to zero in 10 seconds we reduced it to zero in 2 seconds. The current would still be clockwise, but it would be 5 times as large. So, we'd get five times the current for 1/5 of the time - what is the same no matter how fast we make the change, as long as the total change in flux is the same?

For a given change in flux the induced current multiplied by the time there is an induced current is constant.
DQ = I Dt, so the same total charge flows every time.