How to Calculate Magnetic Field for Uniform Surface Current on XOY Plane?

[mmainak]

Homework Statement

am stuck on a magnetic field problem, please help me out..

The XOY plane carries a uniform surface current density k`=50 x^ A/m. What is the magnetic field at the point z = -0.5m?

Homework Equations

Curl B = mu₀J

The Attempt at a Solution

using stokes theorem
Int[Curl B.ds`]=Int[B.dl`]= Int[mu0 J`.ds`]

B. 2.pi.(.5)=50.pi.(.5)^2

i.e B=25 wbbut the answer is given 10pi.10^-6 wb.

 

[Redbelly98]

The problem with using a circle for the closed path integral is that B does not point "around the circle" for a surface current. So ∫B·dl is not simply B·circumference.

Instead, B will point along the same direction everywhere on one side of the surface. What shape does that suggest you should use as the closed path, for calculating ∫B·dl?