Electric field on grounded plane

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SUMMARY

The discussion revolves around calculating the electric field due to a charge Q located above two grounded half-planes in the x-y and x-z planes. The participant initially considered using image charges but questioned the assumption of the planes being conducting. The correct approach involves recognizing that grounding applies to conductors, and the electric field should be evaluated just outside the grounded plane. The final expression for the electric field at the specified point is derived using the method of images.

PREREQUISITES
  • Understanding of electric fields and potentials, specifically in electrostatics.
  • Familiarity with the method of images in electrostatics.
  • Knowledge of grounded conductors and their implications on electric fields.
  • Proficiency in applying Coulomb's law and related equations, such as E=Q/4pi(epsilon)r^2.
NEXT STEPS
  • Study the method of images in electrostatics for complex charge configurations.
  • Learn about grounded conductors and their impact on electric fields.
  • Explore the implications of non-conducting grounded planes on electric potential.
  • Review advanced electrostatics problems involving multiple charges and boundary conditions.
USEFUL FOR

Students in physics, particularly those studying electromagnetism, as well as educators looking to clarify concepts related to electric fields and grounded conductors.

Andrew774
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This question was on our final, but I do not completely understand what the professor was trying to say.

1. Homework Statement

"A charge Q is located at a distance d above an infinitely large grounded half-plane located in the x-y plane and at a distance d from another grounded half-plane in the x-z plane. Find the electric field at a point of coordinates x=y=0 and z=d."

Homework Equations


E=Q/4pi(epsilon)r^2
Phi=Q/4pi(epsilon)r

The Attempt at a Solution


I first thought to use image charges, but he never stated that the plane was conducting, and a nonconducting grounded plane does not necessarily have constant potential. So instead I simply found the electric field as if the plane was not there

E=-Q/4pi(epsilon)d^2 (y hat)

If I had assumed it was a conductor, wouldn't E just equal zero since the point is within the plane?

The rest of the problems on the final took a very long and involved process to solve so either alternative to this question seemed out of place.

How should I have gone about this problem?
 
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Hello and welcome to PF!

Grounding an object only makes sense if the object is a conductor. I assume that the two half-planes meet along the x-axis such that they form the boundary of the region z>0 and y>0.

I guess the question is asking for the electric field just outside the half-plane in the x-z plane. That is, find E at the point (ε, ε, d), where ε→0+.

Method of images sounds good!
 

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