A 5 meter long super conductor carries 100 Amps, and it passes through a 1 Tesla magnetic field at 0.010 seconds, Is EMF = - (BL) / (t)?

And since the resistance of the super conducting wire is zero, shouldn't EMF = 0 based on ohms law?

Now, lets take another wire with R = 0.001 ohms, and the the induced EMF was 1V for example, the current is V/R = 1000 Amps?!

This is confusing because the magnetic resistance(Lenz law) is massive!

  • \$\begingroup\$ What's the question though? \$\endgroup\$ – horta Mar 11 '14 at 3:52
  • \$\begingroup\$ Well there are 2 questions, 1 being if a SC moved around a magnetic field shouldn't -V = 0 since the resistance = 0, thus no current? (Based on ohms law V = IR)? The second one you already answered to it :) \$\endgroup\$ – Pupil Mar 11 '14 at 8:43

I asked a physicist this question. Here's what I understand.

First, Ohm's "law" only applies to ideal resistors. A superconductor is a nearly ideal inductor. That means that its voltage and current are related (to a first approximation) by the equation v=L*di/dt, not by Ohm's law.

Faraday's law still applies to superconductors. A change in magnetic field causes a voltage to appear in the superconductor. This voltage causes current to flow. Because voltage is proportional to the derivative of current, a transient voltage (when integrated) results in an enduring current in a superconducting loop. The current will stick around as long as the magnetic field is present. As the magnetic field is being removed, a voltage transient of the opposite polarity appears, which induces a current in the opposite direction, and when the field is gone, the current in the loop is 0 again.

This voltage is in fact what causes the current to flow -- it's not possible for the current in a superconducting loop to change without some kind of voltage present. When the current is constant (dc), as in a perpetual current loop, the voltage is 0; v=L*di/dt is satisfied.


If you have a power supply to drive 1000 Amps then yes, at 1V through a 0.001 ohm resistive wire, you'll end up with 1000 Amps. Normally, power supply limitations prevent that from happening.

The only thing you seem to be confused about is the asymptotic effect generated by the inverse function 1/x (or V/R in this case).


You're correct as well on your second question. The voltage will be 0 in a superconductor because the resistance is 0. The current does not necessarily have to be 0 though. Once the current starts flowing either through magnetic force or an applied voltage, you'll end up with a current flow that continually persists. This is touched on in the wikipedia article here: "If the voltage is zero, this means that the resistance is zero. Superconductors are also able to maintain a current with no applied voltage whatsoever," http://en.wikipedia.org/wiki/Superconductivity#Zero_electrical_DC_resistance

That current will continue to flow virtually forever until one tries to take energy out of it.

  • \$\begingroup\$ What if a SC, moved around a magnetic field, since R = 0, it will not induce any voltage? Faraday's law is not applied? \$\endgroup\$ – Pupil Mar 11 '14 at 19:09
  • \$\begingroup\$ Right it will never induce a voltage because you'd just make the electron charges move without any resistance so you'd get a current without putting any voltage on it. You could think of it like pushing an object with no mass. It would take no effort and the object would accelerate to whatever speed you could move your hand up to. \$\endgroup\$ – horta Mar 11 '14 at 20:20
  • \$\begingroup\$ How can current flow \$\endgroup\$ – Pupil Mar 12 '14 at 3:24
  • \$\begingroup\$ Current flows because there's no resistance in a SC. Current is simply electron charges moving. For a very brief moment of time the mass of the electrons would resist a change in velocity because they need to be accelerated to whatever speed you want them moving at. That would be the only resistance you would temporarily see. After that very brief time, the electrons would continue to flow because there's no force acting on them (negatively or positively). Electrons have very little mass, so it doesn't take much force to start them moving. \$\endgroup\$ – horta Mar 12 '14 at 14:17
  • \$\begingroup\$ I don't think this answer is correct. To start with, you can't apply Ohm's law to a superconductor. Superconductors have no DC resistance, but they still have reactance, and they still dissipate AC power. Researching now. \$\endgroup\$ – trentcl Apr 11 '14 at 2:43

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