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I am in an introduction to Electricity and Magnetism class and we are using Griffiths. In example 7.8 on page 318, his solution says that the "changing magnetic field induces an electric field". But I solved this example by claiming that the changing magnetic field induces a current. Which is more correct?

The example in the book:

A line charge λ is glued onto the rim of a wheel of radius b, which is then suspended horizontally, as shown in Fig. 7.26, so that it is free to rotate (the spokes are made of some nonconducting material—wood, maybe). In the central region, out to radius a, there is a uniform magnetic field B0, pointing up. Now someone turns the field off. What happens?

screenshot of book's example

enter image description here

My solution: By looking at the equation $\epsilon = -\frac{\partial \Phi}{\partial t}$, we see that the change in flux will cause an emf. So then I thought that maybe I should say that if the $B$ field in the $+z$ direction stopped, then nature will create a current in such a way as to cause a $B$ field in the opposite direction. So this tells me that the "pretend" $B$ field will point downwards and create a current in the $-\phi$ direction. If the current moves in this direction, then the wheel will spin in the opposite direction.

So I get the same answer as the one in the book, but I think my reasoning may be off. Could someone point out the parts of my interpretation that were wrong?

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An electric field, and the electric field can induce a current.

Faraday's law states that

$$ \nabla \times E = -\frac{\partial B}{\partial t}$$ meaning that a change in $B$ induces $E$.

Electromagnetic waves are possible because of this: an alternating current induces an alternating magnetic field which induces an alternating electric field, and that too creates alternating magnetic fields (see Ampere's law with Maxwell's correction) and so on... This is called an "electromagnetic wave" and I just described very very loosely how a radio transmitter works.

Hope it helped!

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  • $\begingroup$ Thank you very much for your help. I have a favor to ask of you: could you please take a look at my solution and give me advice as to how to adjust my argument or point out specifically where my argument fails? $\endgroup$ – loltospoon Feb 27 '17 at 20:24
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Just try to re-use your approach in the following modified setup and you will see why it is best to go with the direct approach ("changing magnetic field induces electric field and the charges interact with electric fields - attracted or repelled; they feel the force!"). Modified setup: The wheel is fixed and cannot rotate!

If you still would like to stick with your approach even in this scenario, you may like to read a little bit about displacement electric field and/or current.

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A changing magnetic field creates a non-conservative electric field in the vicinity. This electric field drives the current in a conductor.

While both the statements are correct, the statement that a changing magnetic field induces an electric current is a special case of the statement that a changing magnetic field induces an electric field.

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