1. PF Contest - Win "Conquering the Physics GRE" book! Click Here to Enter
    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!

Magnetic field of a circular loop

  1. Nov 30, 2015 #1
    1. The problem statement, all variables and given/known data
    A circular loop of radius R is on the xy plane and the center is at the origin, the current is flowing in a counter-clockwise manner. a) Let Q=(a,0,a) be a point such that a>>R. Find Br and Bθ at Q. b) Let Q=(ha,0,0) be a point on the x-axis such that h<1. Find the vector potential A at Q as a power series of h.

    2. Relevant equations
    A(r) = k∫ (J(r') dτ') / |r-r'| = kI ∫ dr' / |r-r'| where k is μo/4π and I is the current

    3. The attempt at a solution
    a) From azimuthal symmetry, we can restrict the situation to points r on the xz plane.
    dr'=(dx', dy', 0)=(-Rsinφ', Rcosφ', 0)dφ'. Since the only non vanishing component of A is Aφ

    Aφ(r) = kI ∫ (Rcosφ' dφ') / |r-r'| from 0 to 2π

    Bφ = 0
    Br = - 1/r ∂/∂cosθ (Aφsinθ)
    Bθ = - 1/r ∂/∂r (rAφ)

    Is this correct?

    For part b) I don't know if it is a multipole expansion or somethin' else... Any help?
  2. jcsd
  3. Dec 1, 2015 #2
    I think for part b) it can be expressed as a multipole expansion, Aφ = kI ∑l=0 ( ha< Pl(0) Pl(cosθ) )/( l(l+1) ). Is this correct?

    Attached Files:

Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted