Induced Electric Fields and EMF

Main Question or Discussion Point

Ok, this may borderline a homework problem, but I'm not quite grasping the concept of induced electric fields. So lets say that they exist a wire loop and solenoid. The switch in the circuit containing the solenoid is originally open and then closed. At this instant, we induce an emf in the loop since we are changing magnetic flux (at this instant). Now since the loop isn't moving, how do the charge carriers move in the loop? Is it by the induced electric field from the change in magnetic flux and we now take into account of the Lorentz force. And by doing this are we saying that the magnetic component of the Lorentz force is zero? Therefore it is the Lorentz force (the electric component) that acts on the charge carriers and causes the current and not a magnetic force exerted by the solenoid (sorry, it's the phrasing my homework uses)?

Since my thoughts tend to be all over the place, here is a summary:

1.) Stationary Loop in a changing magnetic field
2.) We induce an emf by Faraday's Law (changing magnetic flux)
3.) This induced emf is caused by an induced electric field
4.) There is no magnetic force acting on the charge carriers since there is no relative motion of the loop
5.) Taking into account the Lorentz Force, the magnetic component is zero and the force that causes motion of the charge carriers is due to the electric field
8.) Thus the induced current is caused by the induced electric field?

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There are 5 basic laws in action at the same time, and all 5 must hold. They are Ohm's law (OL), Ampere's law (AL), Faraday's law (FL), Lenz' law (LL), and the conservation of energy law (CEL).

1.) Stationary Loop in a changing magnetic field

This condition exhibits induction.

2.) We induce an emf by Faraday's Law (changing magnetic flux)

FL.

3.) This induced emf is caused by an induced electric field

"Cause and effect" is a bad way to look at it. Under time-changing conditions neither the E field nor the H field can exist independently. You can't have one without the other. Likewise under dynamic conditions (time-changing), current and voltage cannot exist independently of one another. You get both or you get neither. There are no known exceptions.

4.) There is no magnetic force acting on the charge carriers since there is no relative motion of the loop

There is still a magnetic force, as no motion is necessary.

5.) Taking into account the Lorentz Force, the magnetic component is zero and the force that causes motion of the charge carriers is due to the electric field

The electric field tends to act in the same direction as the charge motion or velocity. The magnetic field acts normal to the velocity. Both E and H exert influence on the charge. Remember, E cannot exist without H, and vice-versa. They are mutually inclusive.

8.) Thus the induced current is caused by the induced electric field?

Again, a time changing H (magnetic) field cannot exist alone. There is always a non-zero E (electric) field associated with it. Also, the converse is true. Which is the cause and which is the effect is an endless vicious circle.

I hope I've helped. If this gives you trouble, don't feel bad. The most brilliant minds stumble over these issues.

Thanks cabraham!

But I'm still confused on to why there is magnetic force acting on the charges if the loop is stationary relative to the observer?

I still see it as if the conductor is moving relative to the magnet, then the charges are put into motion under a magnetic force, while if the conductor is stationary and the magnet is moving, then the charges are put into motion by an electric force given by qE. Are we really saying that these forces are one of the same, but it just depends on your frame of reference?

Thanks cabraham!

But I'm still confused on to why there is magnetic force acting on the charges if the loop is stationary relative to the observer?

I still see it as if the conductor is moving relative to the magnet, then the charges are put into motion under a magnetic force, while if the conductor is stationary and the magnet is moving, then the charges are put into motion by an electric force given by qE. Are we really saying that these forces are one of the same, but it just depends on your frame of reference?
Although the loop is stationary, the charges moving in the loop, i.e. the current, are not stationary. An H field exerts a force on a moving charge normal to its velocity. As long as the H field is varying with time, no motion of the conductor or magnetic source is necessary.

As far as E and H go, are they "one and the same"? Investigators have studied this question for many generations. Forces due to E and H fields are classified as "electromagnetic". The relation between electric and magnetic forces is so strong, the science community considers them as lumped into one entity. They appear to be, at least to the best of my knowledge, two sides of the same coin. With time we will learn more, but for now all I'm sure of is what Maxwell's equations state. Under time-varying, i.e. dynamic, conditions, E and H fields cannot exist independently. They must both be zero, or both be non-zero. Under static conditions, you can have either one without the other.

As far as reference frame goes, a good paper to read as a primer is Albert Einstein's 1905 paper "On The Electrodynamics Of Moving Bodies". He answers many questions, as well as leaving some unanswered, which is only to be expected. A google search should turn up this paper, which I was able to download for free. If you can't find it, I'll email it to you. BR.

Claude

Wow thanks cabraham for the help. Today we get into Maxwell's equations and the relationship of electricity and magnetism. Hopefully this will give me a better understanding. I'll also check out that paper. Thanks again!