Magnetic field of current loop

  • #1

Homework Statement


Find magnetic field along the z-axis of a circular loop, radius R with constant current lying in the z=0 plane.


Homework Equations


vec(r) = vector of r.
zhat = unit vector z.


The Attempt at a Solution


So starting with the definition, B = (u_o I/4pi) (dl x vec(r))/r^3, where:
\vec(r) = z(zhat) - R(s hat), thus:
r = root(z^2 + R^2)

also dl x vec(r) = vec(r)dl(phi x s) = (dl)(-zhat). Since dl = length around current loop = 2piR:
dl x vec(r) = -2piR(zhat) vec(r).

Here's where I get stuck.
If I continue along this line of thought, zhat (from the cross product) dotted with vec(r) will give me z, and my numerator will end up being -2piRz, but the answer says the numerator should be -2piR^2. Basically, I should have an R instead of z, but I don't know where I'm going wrong. I know other approaches will give me the right answer, but can someone identify along my train of thought what the problem with this approach is?

Thanks,
Ari
 

Answers and Replies

  • #3
I'm looking at it, but judging from the diagram it looks like dBz should equal cosine theta, not sine theta which is what they're claiming.... Still kind of confused.
 
  • #4
Spinnor
Gold Member
2,181
391
I'm looking at it, but judging from the diagram it looks like dBz should equal cosine theta, not sine theta which is what they're claiming.... Still kind of confused.

Draw your own picture. When theta goes to 90 degrees dB = dB_z as required.
 

Related Threads on Magnetic field of current loop

  • Last Post
Replies
1
Views
6K
  • Last Post
Replies
9
Views
6K
  • Last Post
Replies
3
Views
249
Replies
8
Views
4K
  • Last Post
Replies
0
Views
2K
  • Last Post
Replies
8
Views
6K
Replies
9
Views
55K
Replies
2
Views
12K
Replies
2
Views
4K
Replies
6
Views
9K
Top