I posted questions about this subject some time back. Didn't get them answered to my satisfaction, but did learn of an EXCELLENT textbook - E.M.Purcell's Electricity and Magnetism - thanks to you all that responded! Now I have two questions about some of his material.(adsbygoogle = window.adsbygoogle || []).push({});

(1) I waded through his derivations of Ampere's law for PARALLEL currents, and thought I understood them. Once current is flowing in the wire, it sheds electrons until it is neutral again, IN THE LAB FRAME. But then, IN THE ELECTRONS' FRAME, the protons appear Lorentz contracted, so the wire appears positive to parallel moving charges outside the wire, etc.

Sounds good, until you get to a later chapter, where he derives the E-field around a MOVING charge: E'(perpendicular to v) = gamma * E(perp), and E'(parallel to v) = E(para). Obviously the electrons are moving with their drift velocity in the lab frame, so wouldn't the electrons' perpendicular E-field exceed the perpendicular E-field of the stationary protons, and the wire appear to be positive rather than neutral, even in the lab frame?

(2) Then in his derivation of Ampere's law for PERPENDICULAR currents (see page 198), Purcell invokes Gauss' theorem to show that the E-field perpendicular to the wire must remain zero - because there are equal numbers of positive and negative charges per unit length of wire. What?! Isn't Gauss' theorem limited to static charges? Obviously, a wire carrying a current cannot have all the positive and negative charges stationary in ANY reference frame. So is Purcell being careless, or am I missing another subtle point?

Thanks,

BB

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Ampere from SRT again

**Physics Forums | Science Articles, Homework Help, Discussion**