Chronology |
Current Month |
Current Thread |
Current Date |

[Year List] [Month List (current year)] | [Date Index] [Thread Index] | [Thread Prev] [Thread Next] | [Date Prev] [Date Next] |

*From*: Geoff Nunes <gnunes@MAILAPS.ORG>*Date*: Fri, 1 Jun 2001 23:34:38 -0400

Wolfgang Rueckner wrote:

A student asked me a question that I couldn't satisfactorily answer

Perhaps others don't agree, but I have not seen in this discussion

anything that Wolfgang can tell to his student. Here is my attempt

(which I am sure will require "refinement").

First, we have to be very careful to restrict our discussion to circular

paths. This has to do with the fact that knowing the curl of E is not

enough to completely specify E. But if we stick with circular paths

then we can talk about the special solution in which E is constant in

magnitude and purely tangential to the path. This also has the

advantage of being a field that is (relatively) easy to visualize.

Now we can talk about the split loop. Clearly no current flows, so

there is clearly no electric field inside the metal. But we haven't

made dB/dt vanish---that electric field is still there. So there must

be a _second_ electric field which exactly cancels the first (_inside_

the metal). This second field comes from electric charge on the surface

of the wire. In the first picosecond or so after dB/dt was turned on,

the field in the metal was not zero, so charge moved. Once it got to

the surface it could go no further. So it sits there with it's own

electric field acting to cancel the E field from Faraday's law. In the

steady state, this cancellation is complete.

If you think about it for a while, you realize that you need quite an

elaborate arrangement of charge all along the wire. Cancelling the

field at the ends of the wire is easy---it just requires a uniform

sheet. But all that curvature is hard to deal with.

Now let's open up the gap, wider and wider. We'll be careful keep the

remaining wire circular along the original path and always calculate E

from integrating all the way around that path. With a wider gap, the

wire is shorter. That means there is less of the curved part that is so

difficult, so there needs to be less charge on the surface. This

process continues smoothly until the surface charge vanishes at the same

moment the length of wire goes to zero.

[This argument will be more difficult to make to students if you haven't

been teaching them about surface charges on wires, but then my prejudice

is that you should be!]

- Prev by Date:
**AMAZING** - Next by Date:
**Re: Faraday induction** - Previous by thread:
**Re: Faraday induction** - Next by thread:
**Re: Faraday induction** - Index(es):