Magnetic Field from Sheets of Current

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SUMMARY

The discussion centers on calculating the net magnetic field at a point between two infinite sheets of current using Ampere's Law. The left sheet has a current density of 0.19 A per wire with 990 wires/m, while the right sheet carries the same current in the opposite direction. The user initially applied Ampere's Law incorrectly, treating the sheets as line currents rather than surface currents. The correct approach involves recognizing the symmetry of the system, leading to a net magnetic field of zero at the midpoint between the sheets.

PREREQUISITES
  • Ampere's Law
  • Understanding of magnetic fields generated by current-carrying conductors
  • Concept of current density
  • Knowledge of symmetry in physics problems
NEXT STEPS
  • Study the application of Ampere's Law for infinite sheets of current
  • Explore the concept of magnetic field symmetry in current distributions
  • Learn about the differences between line currents and surface currents
  • Investigate the effects of multiple current sources on magnetic fields
USEFUL FOR

Physics students, educators, and anyone studying electromagnetism, particularly those focusing on magnetic fields generated by current-carrying sheets.

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Homework Statement



Two infinite sheets of current flow parallel to the y-z plane. The left-hand sheet, which intersects the x-axis at x = 0, consists of an infinite array of wires parallel to the z-axis with a density n = 990 wires/m and a current per wire of IL = 0.19 A in the +z direction. The right-hand sheet, which intersects the x-axis at x = a = 10 cm, is identical to the left-hand sheet, except that it has a current per wire of IR = 0.19 A in the -z direction.
https://wug-s.physics.uiuc.edu/cgi/courses/shell/common/showme.pl?cc/DuPage/phys2112/summer/homework/Ch-26-B-Force-and-Fields/B-field-from-sheets/0805.gif
Calculate the y-components of the net magnetic field at x = 5 cm

Homework Equations



Ampere's Law: [tex]\mu[/tex]o*I/(2*pi*r)

The Attempt at a Solution



I thought I would only have to use Ampere's Law for each sheet, so my equation looked like this:
B = [tex]\mu[/tex]o(.19)/(2*pi*.05)
I multiplied this answer by two, since they have the same current and are the same distance away, but the solution was incorrect.

Any suggestions?
My only guess is that I'm treating it like a line rather than a sheet, but even if you take dB, it turns out to be the same equation.

Thanks in advance!
 
Last edited by a moderator:
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B = 0
Look for symetry. I'll explain more later. Must sleep.
 

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