# Electric field on grounded plane

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.

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TSny
Homework Helper
Gold Member
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!