Register to reply

Magnetic field of a circular loop of wire

by tjkubo
Tags: circular, field, loop, magnetic, wire
Share this thread:
tjkubo
#1
Apr9-09, 04:03 AM
P: 40
1. The problem statement, all variables and given/known data
I know how to find the magnetic field at the center of a circular loop of wire carrying current. If the radius of the loop is R, how do you find the magnetic field at a distance a from the center of the loop where a<R?


2. Relevant equations
[tex]
d{\mathbf{B}} = \frac{{\mu _0 }}{{4\pi }}\frac{{Id{\mathbf{s}} \times {\mathbf{\hat r}}}}{{r^2 }}
[/tex]


3. The attempt at a solution
The small current element ds is always tangent to the loop. r varies from R-a to R+a. The angle θ between ds and [tex]\mathbf{\hat r}[/tex] seems to vary from 90 to some maximum angle that depends on a.
Also, if you define ϕ to be the angle around P from the place you first start to integrate to ds, then [tex]ds\neq rd\phi[/tex].

This is as far as I can analyze. I have no idea what to do with the angles. I am guessing there is some kind of relationship between r and θ or between r and ϕ or between θ and ϕ that I can't see.
Phys.Org News Partner Science news on Phys.org
World's largest solar boat on Greek prehistoric mission
Google searches hold key to future market crashes
Mineral magic? Common mineral capable of making and breaking bonds
Cyosis
#2
Apr9-09, 04:34 AM
HW Helper
P: 1,495
First thing you want to do is draw a picture and realise this is a highly symmetric problem. From symmetry you can determine the direction of [itex]\boldsymbol{B}[/itex], draw this vector. Then draw the x and y components. Due to symmetry can you tell what the magnitude of [itex]B_y[/itex] will be? Can you express [itex]B_x[/itex] in terms of B?

Why do you think the angle between [itex]d\boldsymbol{s}[/itex] and [itex]\mathbf{\hat r}[/itex] changes? It does not. So [itex]d\boldsymbol{s} \times \mathbf{\hat r}=ds[/itex].

How does the distance r from the loop to a depend on known variables and does the magnitude of B vary when you rotate over the angle [itex]\phi[/itex]?

Try to enter all information into the Bio Savart law now.


Register to reply

Related Discussions
Flux through a loop of wire in a magnetic field. Introductory Physics Homework 3
Magnetic Field at the Center of a Wire Loop Introductory Physics Homework 10
Magnetic Field of wire on rectangular loop Introductory Physics Homework 5
Flux in a Wire Loop w/ a Magnetic Field Introductory Physics Homework 1
Magnetic Field With Loop and Straight Wire Help! Introductory Physics Homework 2