Physics Stack Exchange is a question and answer site for active researchers, academics and students of physics. Join them; it only takes a minute:

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

Suppose you have a uniform ring charge rotating at constant angular velocity so that you also have a uniform ring of steady current, and thus you can use the Biot-Savart Law to compute the magnetic field. But I also remember from college that to good approximation you can use electrostatics to compute the electric field due to the charge if the current is steady, in spite of the fact that charges are moving. I never understood how this works. Can someone offer insight?

share|cite|improve this question
up vote 3 down vote accepted

In the stationary situation all partial derivatives with respect to time vanish (this is in a sense the definition of a stationary state). Looking at the Maxwell equation relevant to determine the electric field, you note that they are given by $$\nabla \cdot \mathbf E = \rho, \qquad \text{and} \qquad \nabla\times\mathbf{E} = -\frac1c\partial_t\mathbf B=0,$$ i.e., the same equations as in the steady state, so you can introduce a potential and reduce the set of equation to Poisson's equation.

share|cite|improve this answer
That's crystal clear. I was anticipating some complex cancellation of first order contributions. It would also seem I was somewhat mistaken in that given ideal sources, the reliability of electrostatics is in fact exact, not just an approximation. That's good to know. – David H Sep 5 '12 at 18:41

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.