Deriving Electric Field Independence on Negligible Separation

Click For Summary
SUMMARY

The electric field between two parallel plates is independent of the separation distance when the separation is negligibly small, as derived using Gauss's Law. By applying Gauss's Law to a sheet of charge, it is established that the electric field is perpendicular to the surface and uniform across the plates. The total electric field between the plates is the sum of the fields from each plate, reinforcing the concept that the field remains constant regardless of distance due to the infinite nature of the plates.

PREREQUISITES
  • Understanding of Gauss's Law
  • Familiarity with electric fields and charge distributions
  • Knowledge of symmetry in electrostatics
  • Concept of infinite planes in physics
NEXT STEPS
  • Study the application of Gauss's Law in different geometries
  • Explore the concept of electric fields from infinite sheets of charge
  • Learn about the behavior of electric fields in capacitor systems
  • Investigate the implications of electric field independence in practical applications
USEFUL FOR

Physics students, electrical engineers, and anyone interested in electrostatics and the behavior of electric fields in various configurations.

spikelau
Messages
1
Reaction score
0
I read from a website that the electric field is independent of the separation between the plates if the separation is negligibly small. But how to derive this?
 
Physics news on Phys.org
Use Gauss's Law

Start by deriving the field close to a sheet of charge. Use Gauss's law, realizing that the electric field, by symmetry, will be perpendicular to the surface.

The field between two parallel plates will be the sum of the fields from each plate.
 
In fact, this is true for a single, infinitely large plane too. And a hand waving argument for why this might be true is that there is no distance scale set by an infinite plane ...i.e. the result should be scale independent. I could use this same argument for a single point charge, or a line charge too...and of course it would be wrong, so don't take it too seriously

But go ahead with the Gaussian pillbox and see what you get.
 
Last edited:

Similar threads

Undergrad Magnetic field when the area of the plates of a capacitor increases
  • · Replies 7 ·
Replies
7
Views
2K
Undergrad Electric Field of Uniformly Charged Infinite Plane
  • · Replies 6 ·
Replies
6
Views
899
High School Curious about the uniform electric field between metal plates
  • · Replies 8 ·
Replies
8
Views
2K
High School Electric Field Created by 2 Infinite Plates
  • · Replies 1 ·
Replies
1
Views
2K
Undergrad What determines if wave components are independent vs coherent?
  • · Replies 3 ·
Replies
3
Views
1K
Undergrad Gauss' Law - Does it apply even when there are external fields?
  • · Replies 9 ·
Replies
9
Views
3K
High School Electric Field Created by a Finite Plate
  • · Replies 2 ·
Replies
2
Views
2K
Undergrad Off resonance driving of a MW/RF cavity
  • · Replies 9 ·
Replies
9
Views
1K
Undergrad Parallel Capacitor safety at 10 micron plate spacing
  • · Replies 32 ·
2
Replies
32
Views
2K
Undergrad Does a time varying magnetic field in vacuum produce electric field or not?
  • · Replies 7 ·
Replies
7
Views
2K