Confusion regarding line integrals

  • #1

Main Question or Discussion Point

Sorry if this is the wrong place to post this, but I wasn't sure where exactly to put it.
When we calculate the force on a closed loop of current-carrying wire in a uniform magnetic field,
We calculate the line integral of the loop to be 0.
However, when we evaluate the line integral for an Amperian loop while using Ampere's law, we integrate from 0 to 2π.
Why is there a difference? I'm not very advanced with calculus, so some intuition is all I request.
 

Answers and Replies

  • #2
kuruman
Science Advisor
Homework Helper
Insights Author
Gold Member
8,568
2,021
I am not sure I understand what you are asking. Both line integrals are taken over closed loops, so if your variable of integration is some angle θ, then the limits of integration would be from 0 to 2π. The fact that the net force on a current loop in a uniform magnetic filed is zero is a different issue. Think of the integral as a sum. In the current loop case you are adding a whole bunch of elements ##d \vec{F}## that point in all sorts of directions so that their sum is zero regardless of the shape of the loop. In the Amperian loop case, you choose the loop so that the B-field is tangent to the loop in which case all the ##\vec{B}\cdot d\vec{\mathcal l}## terms add together to give a non-zero value.

I hope I answered your question.
 

Related Threads for: Confusion regarding line integrals

Replies
2
Views
473
Replies
3
Views
2K
Replies
6
Views
952
  • Last Post
Replies
5
Views
2K
  • Last Post
Replies
1
Views
921
Replies
1
Views
1K
Replies
8
Views
3K
Replies
13
Views
2K
Top