Electromagnetism Help: Calc Electric Field w/ Gauss's Law

[andyfreesty1e]

Homework Statement

Use Gauss’s law to obtain a vector expression for the electric field produced by an
infinte sheet of charge with a surface density of 1 C m−2 , confined to the xy plane. Hence
show that the divergence of this electric field is zero for all points not in the xy plane.

Homework Equations

\int {E.dS} = {Q}/{epsilon}
del.E = rho/epsilon

The Attempt at a Solution

 

[lanedance]

try picking a useful guassian surface

 

[andyfreesty1e]

i still don't really know where to go with it, any other hints you can give?

 

[gabbagabbahey]

Hi andyfreesty1le, welcome to PF!

First figure out what kind of symmetry the charge distribution (and hence the electric field it produces) possesses (e.g. spherical, cylindrical, planar, etc.). Then read your textbook to find examples of what kind of Gaussian surface you would use for problems with that type of symmetry.

 

[andyfreesty1e]

Ok, so according to my textbook, i would use cylindrical gaussian surface. It tells me how to find the electric field, but i can't see how to work out the electric field vector.

 

[gabbagabbahey]

No, you use cylindrical Gaussian surfaces when the charge distribution is cylindrically symmetric. A plane does not possesses cylindrical symmetry.

 

[lanedance]

you could use a cylindrical surface, or a thin rectangular prism surface equivalently

place it so the flat ends of either the cylinder or prism ar parallel to the plane

consider the case when it contains the plane and when it doesn't, then relate the charge contained to the flux through the surface in each case. It may also help to consider wthen the thisness of the prism shrink to infinitesimal

 

[Bill Foster]

Homework Statement

Use Gauss’s law to obtain a vector expression for the electric field produced by an
infinte sheet of charge with a surface density of 1 C m−2 , confined to the xy plane. Hence
show that the divergence of this electric field is zero for all points not in the xy plane.

Homework Equations

\int {E.dS} = {Q}/{epsilon}
del.E = rho/epsilon

The Attempt at a Solution

You can use a cylinder. Or you can use a "box".

Gauss's Law states that the charge inside a volume is equal to the electric field integrated over the surface of that volume.

So you're looking for the electric field.

First, imagine a box being intersected by the charged plane.

Imagine the "height" of the box goes to zero, so we don't have to concern ourselves with the field coming out of the sides.

If the box has dimensions x^2, what is the charge inside it?

Hint: charge density is charge per area. Multiply that by the area enclosed.

Now, integrate the electric field by the surface area of the volume.

Then solve for E.