Find the surface charge density of a perfect conductor

In summary, the problem involves finding the surface charge density of a sphere with radius R made of perfect conducting material in a uniform electric field E. The solution involves using Gauss's Law and constructing the sphere. The relevant equation used is Phi = ERcosTheta, and the surface charge density is found to be equal to Phi multiplied by the permittivity of vacuum. Assistance with constructing the sphere and applying Gauss's Law would be appreciated.
  • #1
MrBoomer
1
0
This is for extra credit not actual homework but I need the points and I would like to understand the subject matter as well so any help would be much obliged.

Homework Statement


There is a sphere with radius R made up of a perfect conducting material in a constant and uniform electric field E. I am tasked to find the surface charge density ρ.

Homework Equations


See #3 for the relevant equations that I used.

The Attempt at a Solution


I am attempting to solve this problem by Gauss's Law. I am almost done, all I need to do is actually construct the sphere...I think.

Since the electric field, E, is 0 in in the sphere the surface charge density is going to be the charge due to the sphere being in the field E.

I assumed [itex]\Phi[/itex] = ERcos[itex]\Theta[/itex] and then assumed that [itex]_{Q}A[/itex] would be the surface charge density (the enclosed charge in the sphere) = [itex]\Phi[/itex]*[itex]_{\epsilon}0[/itex]

However this doesn't help because I didn't construct any sphere and that is where I am lost. That is assuming I am doing this correctly. If I am not please tell me.
 
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  • #2
So I need to construct a sphere and then use Gauss's Law to find the surface charge density. Can anyone help me out with this?
 

FAQ: Find the surface charge density of a perfect conductor

What is surface charge density?

Surface charge density is the amount of electric charge per unit area on the surface of a material. It is typically measured in units of coulombs per square meter (C/m^2).

How do you find the surface charge density of a perfect conductor?

To find the surface charge density of a perfect conductor, you can use the formula: σ = Q/A, where σ is the surface charge density, Q is the total charge on the conductor, and A is the surface area of the conductor. This assumes that the conductor is a uniform, flat surface.

Can the surface charge density of a perfect conductor be negative?

No, the surface charge density of a perfect conductor must always be positive. This is because a perfect conductor has an infinite number of free electrons that can move to the surface to balance out any excess charge.

How does the surface charge density of a perfect conductor affect its electric field?

The surface charge density of a perfect conductor does not affect its electric field. This is because the electric field inside a perfect conductor is always zero, regardless of the surface charge density. The electric field only exists on the surface of the conductor.

Can the surface charge density of a perfect conductor change?

Yes, the surface charge density of a perfect conductor can change if the total charge on the conductor changes. This can happen if the conductor is brought into contact with another charged object or if the total charge is redistributed on the surface of the conductor.

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