1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: Magnetic field of a circular loop of wire

  1. Apr 9, 2009 #1
    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
    d{\mathbf{B}} = \frac{{\mu _0 }}{{4\pi }}\frac{{Id{\mathbf{s}} \times {\mathbf{\hat r}}}}{{r^2 }}

    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.
  2. jcsd
  3. Apr 9, 2009 #2


    User Avatar
    Homework Helper

    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.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook