Take the 2-minute tour ×
Physics Stack Exchange is a question and answer site for active researchers, academics and students of physics. It's 100% free, no registration required.

Suppose an electric field $E=-\nabla \psi$ where $\psi=-Q\ln r$ where $Q$ is just some constant and I have found its harmonic conjugate to be $-Q\theta+c$ where $c$ is some constant. What does it say about the field? I know that if I calculate the field directly from $E=-\nabla \psi$, I get $E=Q/r$ pointing radially outwards, but I am not sure how to interpret the harmonic conjugate found (is it even right?).

Update: I believe I have figured this out now. All the correct information follows from the Cauchy-Riemann equations!

share|improve this question
1  
Your potential looks like the potential of an infinite line charge. So E does not point radially outwards but cylindrically outward. –  Revo Jan 31 '12 at 20:49
    
@Revo, yes, you are right, of course :) I was working in 2D. –  charge Jan 31 '12 at 20:57
1  
@charge: It would be great if you can post your answer. –  Qmechanic Jan 31 '12 at 22:56

1 Answer 1

It gives you an E field which looks like the B field around a current carrying wire. You can think of it as being the solution from a "magnetic current" at the origin. Of course, it is not a single valued function, which has interesting implications I'm sure someone else will elaborate.

share|improve this answer

Your Answer

 
discard

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.