Displacement current inside capacitor

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SUMMARY

The discussion centers on the calculation of displacement current within a capacitor as presented in "Physics for Scientists and Engineers" by Serway and Jewett. The participant critiques the solution manual's approach, which uses the entire Amperian loop area for calculating electric flux, while the correct method should only consider the area of the capacitor plates due to the assumption that the electric field outside this volume is negligible. The derived expression for the magnetic field, B = (μ₀ I r) / (2A), is clarified to apply only for r less than the radius of the capacitor plates, ensuring accurate results.

PREREQUISITES
  • Understanding of Maxwell's equations, particularly the concept of displacement current
  • Familiarity with the principles of electric flux and magnetic fields
  • Knowledge of Amperian loops and their application in electromagnetism
  • Basic proficiency in calculus for interpreting the derived equations
NEXT STEPS
  • Study the derivation of Maxwell's equations in detail
  • Learn about the application of electric flux in different geometries
  • Explore the concept of Amperian loops in various electromagnetic scenarios
  • Investigate the implications of displacement current in capacitive circuits
USEFUL FOR

Students and educators in physics, particularly those focusing on electromagnetism, as well as engineers working with capacitive systems and electromagnetic theory.

issacnewton
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Hi

I have already solved the problem. I just have some doubts about the solution given in the
solution manual. This is "Physics for scientists and engineers" by Serway, Jewett
In the solution for part b) , the author has taken the area of whole Amperian loop while
calculating the electric flux through it. The book itself derives the expression for the displacement current taking only the area of the capacitor plates, which makes sense , since
its probably assumed that the electric field outside the volume between the plates is zero.
So ,in the solution of the problem, the author derives the expression for the magnetic field at a distance r from the center of the capacitor plates as

B=\frac {\mu_{o} I r}{2A}

it doesn't make sense that B increases as r, distance from the center of the capacitors,
increases.
 

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I think I got it, The r at which the author asks for the magnetic field is less than the radius
of the capacitor plates. So we have to consider the area of the amperian loop only.
So problem is solved.
 

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