Deriving Electric Field Independence on Negligible Separation

In summary, using Gauss's Law, it can be derived that the electric field is independent of the separation between two parallel plates if the separation is negligibly small. This is because the field from each plate can be calculated separately and added together, similar to the field from a single, infinitely large plane. However, this hand waving argument may not hold true for other types of charges. To accurately determine the electric field, one should use the Gaussian pillbox method.
  • #1
spikelau
1
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?
 
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  • #2
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.
 
  • #3
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.
 
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1. What is meant by "Deriving Electric Field Independence on Negligible Separation"?

"Deriving Electric Field Independence on Negligible Separation" refers to the process of mathematically determining the electric field strength between two charged particles when the distance between them is so small that it can be considered negligible or insignificant.

2. Why is the concept of negligible separation important in understanding electric fields?

Negligible separation is important because it allows us to simplify the calculation of electric field strength between two particles. It is often used when the distance between the particles is very small compared to the size of the particles, making the calculation more manageable.

3. How is the electric field strength affected by negligible separation?

When the distance between two charged particles is negligible, the electric field strength becomes independent of the separation distance. This means that the electric field strength will remain the same regardless of how close or far apart the particles are.

4. What is the equation for deriving electric field independence on negligible separation?

The equation for deriving electric field independence on negligible separation is E = (kq)/d^2, where E is the electric field strength, k is the Coulomb's constant, q is the charge of the particles, and d is the distance between the particles.

5. Can the concept of negligible separation be applied to all electric field calculations?

No, the concept of negligible separation can only be applied to calculations involving two point charges. If the charges are not point charges or if the distance between them is not small enough to be considered negligible, this concept cannot be applied.

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