# Lenz's law, does magnetic flux as measured in Tesla decrease when current is induced?

Wikipedia defines Lenz's law as that the magnetic field created by the induced current opposes changes in the initial magnetic field,

"Lenz's law states that the direction of the electric current induced in a conductor by a changing magnetic field is such that the magnetic field created by the induced current opposes changes in the initial magnetic field. "

This seems to imply that the magnetic flux as measured in Tesla should decrease when a current is induced. Does it?

• Magnetic field is measured in Tesla (T). Magnetic flux (which is way Lenz's law addresses) in measured in T$\cdot$m$^{2}$—magnetic field times area.
– Buzz
Jun 6 at 1:44

Yes, and it is possible to test it.

Take two inductors with a steel rod inside, so that both are around the rod. When one of the inductors is connected to the AC supply, and the ends of the other are separated, the rod become a magnet.

When the ends of the second inductor are connected, (so that a current is induced there) the strength of the magnet clearly decreases.

Attention: the impedance of the inductors must be big enough to avoid a huge current (short circuit).

This seems to imply that the magnetic flux as measured in Tesla should decrease when a current is induced. Does it?

Sort of. Consider a situation in which you have, say, a solenoid and a bar magnet. The solenoid is situated upwards and is sitting on a table top. Suppose now that you take a bar magnet with the north pole facing down (toward the top of the solenoid) and you move the bar magnet even closer to the solenoid. By moving the bar magnet closer to the solenoid, you are increasing the magnetic field through the solenoid. Thus the magnetic flux increases as $$\Phi_B=\vec{B}\cdot\vec{A}$$ The flux increases as it is proportional to the magnetic field strength. The induced magnetic field (by Lenz's Law) will point upward to oppose the increasing field downward through the solenoid. This magnetic field will be induced by a counter-clockwise current in the solenoid.

Back to the original question then, does the magnetic flux decrease when the current is induced? I would ask: From what baseline? In this example, I've shown that the magnetic flux through a surface can actually increase from its initial measurement despite Lenz's Law (though Lenz's Law does perhaps prevent a greater increase).

When thinking about problems involving fields, fluxes, and Lenz's Law, initial conditions make all the difference.

As a side note, you specifically mentioned units of Tesla. I would add that the units are irrelevant. The answer is fundamental and does not depend on the units involved.