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

Click For Summary
SUMMARY

The discussion focuses on calculating the magnetic field generated by a uniform surface current density of k' = 50 A/m on the XOY plane at a point z = -0.5m. The initial approach using Stokes' theorem and a circular path integral led to an incorrect result of B = 25 Wb. The correct method involves recognizing that the magnetic field direction remains consistent on one side of the surface, suggesting a different closed path for the integral. The accurate magnetic field value is determined to be B = 10π x 10^-6 Wb.

PREREQUISITES
  • Understanding of Stokes' theorem in electromagnetism
  • Familiarity with the concept of surface current density
  • Knowledge of magnetic field calculations using Ampère's law
  • Proficiency in vector calculus, particularly line integrals
NEXT STEPS
  • Study the application of Stokes' theorem in electromagnetic problems
  • Learn about the derivation of magnetic fields from surface currents
  • Explore Ampère's law and its applications to different geometries
  • Investigate the relationship between current density and magnetic field strength
USEFUL FOR

Physics students, electrical engineers, and anyone studying electromagnetic theory, particularly those focused on magnetic fields generated by surface currents.

mmainak
Messages
8
Reaction score
0

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.
 
Last edited:
Physics news on Phys.org
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?
 

Similar threads

  • · Replies 9 ·
Replies
9
Views
2K
Replies
4
Views
2K
  • · Replies 1 ·
Replies
1
Views
1K
  • · Replies 7 ·
Replies
7
Views
2K
Replies
8
Views
2K
  • · Replies 5 ·
Replies
5
Views
1K
Replies
3
Views
1K
Replies
7
Views
2K
  • · Replies 2 ·
Replies
2
Views
2K
  • · Replies 3 ·
Replies
3
Views
2K