Electric field in and around an infinite sheet of charge.

[morangta]

Homework Statement

Given an infinite, planar, non-conducting sheet of charge with thickness t. The volume charge density ρ is uniform. A conducting plate, held at a fixed potential V=0V, is placed parallel to the sheet at a distance d. Calculate the electric field E at all points, in all four (4) regions of the configuration.

Homework Equations

σ=εE.

The Attempt at a Solution

Given the infinite, parallel structure, all the lines of force E are parallel and normal to the sheet. Placing a cylindrical pillbox parallel to the lines of force with an end at the surface of the sheet opposite to the conductor and the other end in the sheet, use Gauss' Law σ=εE.

I could work this problem, but I don't know how to show that the electric field in the region outside the sheet and away from the conductor has a zero electric field.

Then the number of unknowns would reduce to one (1) when the pillbox is applied to the sheet.

 

[Simon Bridge]

Try working out the potential.

You will need to use your understanding of how the conducting plate affects the potential.
The plate is maintained at 0V with respect to what?

 

[morangta]

It's not w.r.t. the sheet. I thought about making it w.r.t. Earth, but Earth isn't infinite like the sheet and planar conductor are. How about infinity? Does that make sense? If it doesn't, I hope you educate me on this. Thanks for responding. Regards, Ted

 

[Simon Bridge]

Well you have to pick one ... wrt infinity would be the usual one.
It could also indicate that the reference point for voltage is the plate itself.

Without the plate, where would you normally put zero-volts?

Anyway - that is what prompted me to suggest that you use some sort of potential based calculation like Poisson's equation. IN those the reference point for voltage is arbitrary.

You should be able to sketch the electric field lines in for simple arrangements of charges and grounded conductors, and use that knowledge to hep figure out what to do.

 

[morangta]

Use Gauss' Law / Diagram of Regions Between & Outside Sheet and Plate

Simon, the problem intends for the student to use Gauss' Law.

The Gauss pill boxes indicate that the E's are constant in Regions 1 and 4.

x= -∞ x=0 x=d x=d+t x=∞
<---------------->< ----------->< --------------->< --------------------------->
... Region 1 ... |...Region 2 ...|... Region 3 ... |.... Region 4 .....
| ++++++++++++++
Conducting Charged
Plate Sheet (ρ)
V=0V

 

[Simon Bridge]

Presumably the problem also requires you to use your understanding of the physics as well as apply a named procedure.

What form is the electric field likely to be inside the sheet of charge?

What is the overall symmetry of the system? - use this to set up axes and define your regions more clearly.
You know what the electric field due to the charged sheet would be by itself right?
How would the conductor be charged?

 

[morangta]

Thank you to Simon for guiding me to a solution to the sheet charge problem I posted. He was most helpful.

 

[Simon Bridge]

No worries, and well done.