# Voltage across an inductor contradicts Lenz's law?

Imagine a simple circuit consisting of an alternating current source connected to an inductor. Assume they are connected in the following fashion: AC source - terminal A - Inductor - terminal B - AC source. When the current flows from terminal A towards terminal B and is increasing, the inductor should generate electromagnetic force that opposes the increase in current (according to Lenz's law), that is terminal B should become positive with respect to terminal A. But simulation shows the opposite is true. Terminal A becomes positive with respect to terminal B. Why?

the inductor should generate electromagnetic force that opposes the increase in current (according to Lenz's law)

To be sure, it's electromotive force (emf) here and not electromagnetic force.

But simulation shows the opposite is true. Terminal A becomes positive with respect to terminal B. Why?

The voltage across the inductor is the opposite sign of the emf

$$v_L = L \frac{di}{dt} = -\mathcal E$$

and the circuit simulator gives the voltage across.

To see that this must be so, consider connecting an inductor across a voltage source; the voltage across the inductor equals the voltage across the source.

Since the inductor is (usually) a coiled conductor, there is (effectively) no resistance to limit the current through the conductor. How then can there not be an arbitrarily large (effectively infinite) current through the conductor?

The only way for there not to be an arbitrarily large current is for there to be an emf that precisely opposes the applied voltage.

And, since the emf is proportional to the rate of change of current, the current must be changing at a particular rate in order for the generated emf to precisely oppose the applied voltage.

• So the voltage measured across an inductor and the emf generated by this inductor are two different things and they are always equal in magnitude so they cancel each other? Jun 21, 2014 at 17:09
• @Armadillomon, the first part is correct and the second part is correct if we ignore non-ideal aspects of physical inductors. The crucial point to remember is that, in a good conductor, the electric field inside effectively vanishes. Thus, free charge within the conductor will redistribute in such a way that the conservative electric field from the charge distribution effectively cancels the non-conservative electric field (induced by the changing magnetic field threading the inductor) within the conductor. So, there are two contributions, two different 'things'. Jun 21, 2014 at 17:44
• @Armadillomon Correct statement would be " the voltage measured across an inductor, voltage applied across inductor and the emf generated by this inductor are three different things and; voltage applied and emf induced by inductor are always equal in magnitude so they cancel each other in an ideal case. May 4, 2016 at 3:33