Electric field on grounded plane

In summary, the question asks for the electric field at a point on the x-z plane, where one half-plane is grounded and the other is a distance d away. The attempt at a solution involved using the method of images, but it was unclear whether the half-plane was conducting or non-conducting. The final solution involved finding the electric field as if the plane was not there, which resulted in a non-zero value. The question raised the issue of whether the electric field would be zero if the half-plane was a conductor.
  • #1
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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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  • #2
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!
 

1. What is an electric field on a grounded plane?

An electric field on a grounded plane refers to the distribution of electric charges on a flat surface that is connected to the ground. The ground acts as a reference point for the electric field and helps to neutralize any excess charges on the plane.

2. How is the electric field on a grounded plane calculated?

The electric field on a grounded plane is calculated using the formula E = σ/ε, where E is the electric field strength, σ is the surface charge density, and ε is the permittivity of the medium. This formula takes into account the distance from the plane and the type of material the plane is made of.

3. What factors affect the strength of the electric field on a grounded plane?

The strength of the electric field on a grounded plane is affected by the distance from the plane, the size and distribution of charges on the plane, and the properties of the surrounding medium. It is also influenced by the presence of other nearby electric fields.

4. Can the electric field on a grounded plane be manipulated?

Yes, the electric field on a grounded plane can be manipulated by changing the surface charge density or the distance from the plane. It can also be altered by placing other conductive materials near the plane or by introducing external electric fields.

5. What are the practical applications of understanding the electric field on a grounded plane?

Understanding the electric field on a grounded plane is essential in various areas such as electrical engineering, telecommunications, and electronics. It is also crucial in designing lightning protection systems and in the study of atmospheric electricity. Additionally, knowledge of the electric field on a grounded plane is necessary for understanding the behavior of charged particles in a vacuum, such as in particle accelerators.

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