Current in an infinite current sheet

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SUMMARY

The discussion focuses on the application of Ampere’s law to an infinite current sheet with surface density σ. It clarifies that the enclosed current I can be expressed as I = σL, where L is the length of the rectangular loop. The participants confirm that this formulation is correct, as surface current density σ has units of A/m, and when multiplied by length (m), it results in current (A). This ensures that the right-hand side of the equation maintains consistent units.

PREREQUISITES
  • Understanding of Ampere’s law
  • Familiarity with surface current density concepts
  • Knowledge of units in the SI system
  • Basic principles of electromagnetism
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  • Study the derivation of Ampere’s law in different geometries
  • Explore the implications of surface current density in electromagnetic theory
  • Investigate the relationship between current density and electric fields
  • Learn about the applications of infinite current sheets in physics
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Physics students, electrical engineers, and anyone studying electromagnetism or current density concepts will benefit from this discussion.

chipotleaway
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Suppose we have a infinite current sheet of surface density \sigma and apply Ampere’s law to find the magnetic field. Using a rectangular loop of side lengths L, why would the enclosed current be I=\sigma L? Doesn't this imply the RHS has units of \frac{Q}{m}?

Shouldn't we be looking at this: I=\frac{dQ}{dt}=\sigma \frac{dA}{dt}?
 
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A surface current density has units of A/m in the SI system. Multiplying that by length (units of m) gives current (units of A).
 
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