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.

According to Ampere's Ciruital Law:

enter image description here

Now consider two straight wires, each carrying current I, one of infinite length and another of finite length l. If you need to find out magnetic field because of each, at a point (X) whose perpendicular distance from wire is d.

You get magnetic field as $\frac{\mu I}{2 \pi d}$. Same for both.

But,

Magnetic field due to infinitely long wire is : $\frac{\mu I}{2 \pi d}$

Magnetic field due to wire of finite length l : $\frac{\mu I (\sin(P)+\sin(Q)) }{2 \pi d}$, where P & Q are the angles subtended at the point by the ends of the wire.

Why are we getting wrong value for using Ampere's circuit law?

share|improve this question
    
I try to check back on things like this, but to insure attention you can flag the post for the moderators. –  dmckee Aug 31 '11 at 16:34
add comment

1 Answer

up vote 0 down vote accepted

There are two things to notice here.

  1. You can only make the assignment $\oint \mathbf{B} \cdot dl = 2 \pi d B(d)$ if the situation is radially symmetric.
  2. In the case of a finite wire you either have charge building up at the ends or you have not specified the whole current distribution yet. Question: can you specify a radially symmetric return path and if so do you expected it make up the difference?
share|improve this answer
add comment

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.