The square in the previous example, with sides of length 2 m and in a magnetic field of
strength 10 T, is rotated by 60º in the course of 4 s. What is the induced emf in the square?
In what direction does the current flow?We established in the previous example that the change in flux as the square is rotated is
–20 Wb. Knowing that it takes 4 seconds to rotate the square, we can calculate the
induced emf using Lenz’s Law:
As for determining the direction of the current, we first need to determine the direction of
the change in magnetic flux. From the diagram we saw in the previous example, we see
that the magnetic field lines, B, move in the upward direction. Because we rotated the
square so that it is no longer perpendicular to the field lines, we decreased the magnetic
flux. Saying that the magnetic flux changed by –20 Wb is equivalent to saying that the
flux changed by 20 Wb in the downward direction.
The direction of the current must be such that it opposes the downward change in flux. In
other words, the current must have an “upward” direction. Point the thumb of your right
hand upward and wrap your fingers into a fist, and you will find that they curl in a
counterclockwise direction. This is the direction of the current flow.
Conservation of Energy
Lenz’s Law is really a special case of the conservation of energy. Consider again the bar
sliding on rails. What would happen if the induced current did not oppose the change in
flux?
Since the current flows counterclockwise, the current in the bar flows toward the top of
the page. Thus, the magnetic field exerts a leftward force on the bar, opposing the
external force driving it to the right. If the current flowed in the other direction, the force
on the bar would be to the right. The bar would accelerate, increasing in speed and kinetic
energy, without any input of external energy. Energy would not be conserved, and we
know this cannot happen.
Changing the Flux by Changing the Magnetic Field
So far, we have changed the magnetic flux in two ways: by increasing the size of the
circuit and by rotating the circuit in a constant magnetic field. A third way is to keep the
circuit still and change the field. If a permanent magnet moves toward a loop of wire, the
magnetic field at the loop changes.