Uniform field between parallel plates

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Discussion Overview

The discussion revolves around the nature of the electric field between charged parallel plates, particularly addressing the uniformity of the field and the forces acting on charges within that field. Participants explore theoretical concepts, mathematical reasoning, and the implications of different charge distributions.

Discussion Character

  • Exploratory
  • Technical explanation
  • Mathematical reasoning
  • Debate/contested

Main Points Raised

  • One participant questions the assumption that the electric field is uniform between parallel plates, suggesting that the force on a charge would increase as it moves closer to the positive plate.
  • Another participant clarifies that moving towards a plate is not analogous to moving towards a point charge, prompting further exploration of the nature of electric fields.
  • There is a discussion about the analogy of charged plates to line charges and point charges, with some participants noting that the electric field from a charged plane is uniform, unlike that from point or line charges.
  • Calculus is suggested as a method to demonstrate how the electric field from a line charge falls off as 1/r, with references to external resources for further understanding.
  • Participants discuss the components of the electric field and the role of angles in calculating field strength, with some expressing satisfaction with the explanations provided.
  • One participant inquires about extending the concept of a line charge to a plane, suggesting the use of concentric rings of charge to model the electric field of a plate.

Areas of Agreement / Disagreement

Participants express differing views on the uniformity of the electric field between parallel plates, with some accepting the uniform field concept while others challenge it based on their understanding of forces acting on charges. The discussion remains unresolved regarding the implications of these differing perspectives.

Contextual Notes

Participants express uncertainty about the mathematical derivations involved in understanding electric fields, particularly in relation to the assumptions made about charge distributions and the nature of forces acting on charges.

Who May Find This Useful

This discussion may be of interest to students and educators in physics, particularly those exploring electric fields, charge distributions, and the mathematical principles underlying these concepts.

RK1992
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Hey,

I've recently been studying electric fields, and our teacher told us that the field is approximately uniform between two charged parallel plates, ie the force acting on a unit charge is equal everywhere.

This doesn't seem to tie with everything else we've been taught; surely, as you move an electron toward the positive plate, the force of attraction would increase. We've been told to "accept it" without any real explanation, and I'm not seeing the reasoning behind it on my own..

Is anyone able to help me out?

Thanks
 
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RK1992 said:
surely, as you move an electron toward the positive plate, the force of attraction would increase.
Why do you think that? Note: Moving towards a plate is not quite the same thing as moving towards a point charge.
 
I didn't know that... but why not, surely it's like a line of point charges?
 
It is due to the capacitor having a homogeneous electric field. Imagine this:

You have a positive plate - the closer to the plate you place a body with a negative charge, the bigger the attraction force.
Now imagine placing a negative plate opposite to the positive plate that the negatively charged body is between the plates. The negative plate exerts a repulsion force to the body. The closer the body to the negative plate, the bigger the force.

Say the body is exactly in the center of the plates. The attraction and repulsion forces are equal if the plates have equal but opposite charges, and add up.
Now move the body towards the positive plate. The attraction force increases. As it moves away from the negative plate, the repulsion force decreases. The sum of the two stays the same.
 
RK1992 said:
I didn't know that... but why not, surely it's like a line of point charges?
No, but you're getting closer! The field from a point charge falls off as one over distance squared, that from a line charge as one over distance, but the field from a charged plane is uniform.
 
Doc Al said:
No, but you're getting closer! The field from a point charge falls off as one over distance squared, that from a line charge as one over distance, but the field from a charged plane is uniform.

Is there any way of showing it falls as 1/r ? Seems weird, I don't want to just accept that it does.. I know some calculus, I'm guessing that it will be involved as a sum of infinitely small charges along a line but I'm not sure how to prove it to myself :s
 
RK1992 said:
Is there any way of showing it falls as 1/r ? Seems weird, I don't want to just accept that it does.. I know some calculus, I'm guessing that it will be involved as a sum of infinitely small charges along a line but I'm not sure how to prove it to myself :s
You can certainly use calculus to show that the field from a line charge falls off as 1/r (see: http://hyperphysics.phy-astr.gsu.edu/hbase/electric/elelin.html#c1"). It's a good exercise. (The easy way to show it is to use Gauss's law.)
 
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RK1992 said:
But I have no idea why there is a z/r on the end of their equation for the field strength...
They want the component of the field perpendicular to the line (what they call the radial part of the field). The z/r represents cosθ, where θ is the angle that r makes with the normal to the line. (Study the diagram.)
 
cdotter said:
This website explains it a little better.

http://faculty.wwu.edu/vawter/PhysicsNet/Topics/ElectricForce/LineChargeDer.html

cos(θ) = electric field in the y direction. θ isn't given but cos(θ)=y/r. y is constant (and can therefore be moved outside of the integral). r is found by the pythagorean theorem.

Ah okay, that's a nice explanation :)

Doc Al said:
They want the component of the field perpendicular to the line (what they call the radial part of the field). The z/r represents cosθ, where θ is the angle that r makes with the normal to the line. (Study the diagram.)
Yeah I get it now :D

So I'm now happy with the idea of a line's field varying with 1/r.. how does this tie in with two parallel plates? Is it necessary to do another integral in another direction to extend the line into a plane?
 
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  • #10
RK1992 said:
So I'm now happy with the idea of a line's field varying with 1/r.. how does this tie in with two parallel plates? Is it necessary to do another integral in another direction to extend the line into a plane?
I would consider the field from a ring of charge, then view a plate as a set of concentric rings.
 

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