Derive the Electric Field Outside an Ideal Conductor

In summary, the conversation discusses deriving the electric field outside an ideal conductor without using Gauss's law. The solution involves using the superposition principle and the knowledge that the electric field within a conducting material is zero. By making the vector sum of all electric fields inside the conductor equal to zero, the electric field just outside the conductor can be derived.
  • #1
ladyrx2020
4
0

Homework Statement


Begin from the expression of the electric field outside an infinite sheet of uniform surface charge density, [itex]E=\frac{σ}{2\epsilon}[/itex]. Derive the electric field just outside an ideal conductor: [itex]E=\frac{σ}{\epsilon}[/itex]. Do NOT use Gauss's law.


Homework Equations


Not sure.


The Attempt at a Solution


Any tips on how I can solve this problem?

NOTE:
I removed my attempt at a solution, but I did try.
 
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  • #2
Hi, I think you just use superposition principle in electric field. Imagining that there are two ideal wires in parallel with the current flowing in the opposite direction. Then the electric field between two wires is calculated as follows:
E = E1 + E2
where E1, E2 is the electric field of each ideal wire at the said point.
They have the same value but opposite direction.
E1 = E2 = σ/2ε
I think it is a bit like the electric field between two plates of capacitor.
attachment.php?attachmentid=60140&stc=1&d=1373349736.jpg

It is my opinion, maybe I am wrong.
 

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  • #3
Anhnha's advice should put you on the right track; it's not exactly the same as a parallel plate capacitor, but the idea is very similar.

The key bit of knowledge for this particular problem is that the [static] electric field within the conducting material itself is zero. So you need to make the vector sum of all electric fields inside the conductor add to zero (some electric fields may be originating from charges located somewhere else, such as the opposite side of the conductor or whatnot [it doesn't really matter where the other charges are] -- whatever the case, all electric fields must all sum to zero inside the conductor). By doing so, what then is the electric field just outside the conductor? :wink:
 
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1. What is an ideal conductor?

An ideal conductor is a material that allows electric charges to move freely without any resistance. In other words, it has infinite conductivity and zero resistivity. In reality, no material can be a perfect conductor, but some materials such as metals come close to being ideal conductors.

2. How is the electric field outside an ideal conductor derived?

The electric field outside an ideal conductor can be derived using Gauss's Law. This law states that the electric field passing through a closed surface is equal to the total charge enclosed by that surface divided by the permittivity of the medium. By applying this law to a closed surface surrounding an ideal conductor, we can determine the electric field outside the conductor.

3. What is the direction of the electric field outside an ideal conductor?

The direction of the electric field outside an ideal conductor is always perpendicular to the surface of the conductor. This is because the charges in an ideal conductor are free to move and will always arrange themselves in such a way that the electric field inside the conductor is zero. Therefore, the electric field outside the conductor is directed away from the surface.

4. Does the shape or size of the conductor affect the electric field outside?

No, the shape or size of an ideal conductor does not affect the electric field outside. This is because the electric field outside the conductor is determined by the total charge enclosed by a closed surface surrounding the conductor, not the shape or size of the conductor itself.

5. Is the electric field outside an ideal conductor always zero?

No, the electric field outside an ideal conductor is not always zero. It is only zero in electrostatic equilibrium, meaning there is no net movement of charges. If there is a changing electric field or a non-uniform charge distribution, then the electric field outside the conductor will not be zero.

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