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Q & A: sources of electric field

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Most recent answer: 03/12/2010
Q:
There are two type of electric field : one due to charges and other due to changing magnetic field. My question is that why we don't call the field generated due to changing magnetic field as a new field say a T field why we call the total as electric field. Another thing which has been worrying me for a long time is : why this T field is divergenless(its curl is -dB/dt ) and if the consider the whole thing as electric field then will the formulas derived for E field using coulomb's law remain valid. Ex: formula for energy stored in electric field. Thanks for reading this long stuff.
- dipendra (age 19)
india
A:
The last part of your question really has the answer to the first part. The effects of an electric field on a charged particle don't depend on whether the source is a static charge or a changing magnetic field. Either causes the same acceleration. The energy density of the electric field also doesn't depend on the source. You have to add the fields from all sources then square the result to get the energy density.  It would just complicate things to call the field by two names. The energy density would have three parts: one from each field plus another from their product.

Mike W.

(published on 03/11/2010)

Follow-Up #1: Divergence in Non-Conservative Electric Fields

Q:
But why the non conservative electric field is divergenless?
- ankesh (age 21)
delhi
A:
Hi Ankesh-

I think what you're pointing out is that E can be broken up into two parts, EC and EN, where the curl of
EC is zero (so it's conservative) and the divergence of EN is zero. How does that work? Look at the divergence of E. You can get a field, EC with exactly that same divergence from a static charge distribution proportional to the divergence. However, any field produced by a static charge distribution is just given by minus the gradient of the potential. It's conservative, i.e. the curl of a gradient is zero. Now let E - EC = EN. Since curl of EC =0, curl of EN = curl of E. However, divergence of E= divergence of E -divergence of EC=0. So we've broken up E  into a conservative part EC with no curl and a non-conservative part EN with no divergence.

Becca +mbw

(published on 03/12/2010)

Follow-up on this answer.