Magnetic Field Inside a Charging Capacitor

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SUMMARY

The discussion focuses on calculating the magnetic field strength inside a charging parallel-plate capacitor with a diameter of 10 cm and a spacing of 1.0 mm, where the electric field is increasing at a rate of 1.4×106 V/m·s. The correct formula to use is derived from Maxwell's equations, specifically \(\oint B \cdot ds = \mu \epsilon \frac{dE(t)}{dt} A\). The initial attempt yielded an incorrect magnetic field strength of 7.2E-13 T due to misapplication of the area in the integral, highlighting the importance of using the correct area enclosed by the integral.

PREREQUISITES
  • Understanding of Maxwell's equations
  • Familiarity with parallel-plate capacitor configurations
  • Knowledge of magnetic field calculations
  • Proficiency in calculus, particularly integrals
NEXT STEPS
  • Study the derivation of Maxwell's equations in electromagnetic theory
  • Learn about the behavior of electric fields in capacitors
  • Explore the relationship between changing electric fields and induced magnetic fields
  • Practice solving problems involving magnetic fields in dynamic electric fields
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Students studying electromagnetism, electrical engineers, and physicists interested in the behavior of magnetic fields in capacitors and dynamic electric fields.

Plasmosis1
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Homework Statement


A 10-cm-diameter parallel-plate capacitor has a 1.0 mm spacing. The electric field between the plates is increasing at the rate 1.4×106V/m*s.
What is the magnetic field strength 2.7cm from the axis?

Homework Equations



\ointB*ds=\mu\epsilondE(t)/dt*A
B=(\mu\epsilondE(t)/dt*A)/(2\pir)

B=(\muId)/(2\piR2)*r

The Attempt at a Solution


I tried using the first equation:
8.85E-12*4\piE-7*1.4E6*\pi(0.05)2/(2\pi*0.027)=
7.2E-13T which is wrong
 
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"A" should be the area your integral encloses, not the total area of the capacitor.
 
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