Divergence of B, circular current loop

  • Thread starter pobro44
  • Start date
  • #1
11
0

Homework Statement


[/B]
∇ * B = 0 and ∇ X B = Mu * J. This is proved to hold not only for infinite wires but for magnetostatics in general.

Magnetostatics = steady current

Closed wire loop with constant current is certainly a magnetostatics example.

Magnetic field on z axis above loop around origin is: B = (Mu* I * R^2)/(2 * (R^2 + z^2)^(3/2)) in z hat direction


Homework Equations



Partial derivative with respect to z gives a non zero answer. Divergence is not zero. I am missing something obvious but fail to see what.

The Attempt at a Solution

 

Answers and Replies

  • #2
TeethWhitener
Science Advisor
Gold Member
2,254
1,764
Divergence is not just the partial derivative along z. Really think about the meaning of ##\frac{\partial \mathbf{B}_x}{\partial x}## and ##\frac{\partial \mathbf{B}_y}{\partial y}##.
 
  • #3
rude man
Homework Helper
Insights Author
Gold Member
8,021
857
Can also use cylindrical coordinates to verify ∇⋅B = 0. Look up the formula for div in cylindrical coordinates and apply to the problem.
 

Related Threads on Divergence of B, circular current loop

  • Last Post
Replies
5
Views
1K
Replies
1
Views
1K
Replies
3
Views
2K
Replies
1
Views
682
Replies
12
Views
815
  • Last Post
Replies
8
Views
651
  • Last Post
Replies
3
Views
6K
Replies
3
Views
4K
  • Last Post
Replies
8
Views
2K
Top