Back EMF Paradox: Is There a Contradiction?

[Conservation]

Correct me if I am wrong.

For a RL circuit, I know as a fact at t=0, there is a back emf that is almost equivalent to the original emf source. In order for the back emf to exist, there needs to be a magnetic field in the inductor. In order for there to be a magnetic field in the inductor, there needs to be a current flowing through the inductor. In fact, the current would need to be close to the maximum current to induce such a large back emf noticeable at t=0. Yet, at t=0, I also know that the current in an RL circuit is 0. And so on.

Is this a paradox? What did I miss here?

 

[Dale]

In order for the back emf to exist, there needs to be a magnetic field in the inductor.

This is incorrect. A magnetic field in an inductor does not produce any EMF. A good example is a superconducting MRI magnet where very large magnetic fields exist with no back EMF whatsoever.

A back EMF opposes a change in the magnetic field, not a static magnetic field. To get a large back EMF you need a large change in the field, which is, in fact, what you get in a RL circuit at t=0.

 

[Conservation]

Hm...

The way that I learned back emf is that it is the induced emf from the changing magnetic field in the inductor. (Sorry, didn't say changing in OP) It makes sense that there would be a maximum back emf at the point of maximum rate of change of current, t=0; but to your definition, what accounts for the physical existence of a back emf? Without a current in the inductor, I don't see how there can be back emf.

Also, isn't a superconductor a bad example (Meissner effect)?

 

[Dale]

The way that I learned back emf is that it is the induced emf from the changing magnetic field in the inductor. (Sorry, didn't say changing in OP) It makes sense that there would be a maximum back emf at the point of maximum rate of change of current, t=0;

Then it sounds like you learned it correctly, but simply are not applying it correctly. The basic equation for an inductor is $v=L \; di/dt$. The actual value of i is not relevant, only the time rate of change of i.

but to your definition, what accounts for the physical existence of a back emf?

Faraday's law accounts for the back emf.

Also, isn't a superconductor a bad example (Meissner effect)?

In an inductor, including a superconducting inductor, the magnetic field goes around the wire, not through it. So the Meissner effect doesn't prevent a superconducting coil from acting like a big inductor. The point is that Faradays law, applied to a superconductor, allows a large field/current to exist without any EMF. It is only when you are changing the current that you get an EMF.

 

[PJC01]

The Back EMF paradox can seem confusing at first, but it is not a contradiction. It simply highlights the complex relationship between voltage, current, and magnetic fields in an RL circuit. When the circuit is first turned on, the inductor resists the change in current by producing a back EMF, which is equal in magnitude to the applied EMF. This is why the current is initially 0, as the back EMF is cancelling out the applied EMF. However, as the current gradually increases, the back EMF decreases and the current can flow freely. This is why the back EMF is only noticeable at t=0, when the current is changing rapidly. It is important to remember that the back EMF is a result of the changing current, not the other way around. So, there is no contradiction here, just a complex relationship between different components in the circuit.