How Do Conducting and Non-Conducting Objects Affect Electric Fields?

[Fjolvar]

I have a few questions related to finding the electric field of an object.

1. What's the difference between a conducting object (sphere, cylinder) vs. a non conducting object? Is the charge inside a conducting and nonconducting sphere both zero if the surface charge density is uniform? What about for a cylinder?

2. When you calculate the E field, sometimes I'm given the volume charge density and sometimes the surface charge density. This only means that Qenc is defined by \rho d \tau and \sigma dA correct? Otherwise the concepts are the same..?

Also, I'm looking at a problem from my book using a cylinder where the E field inside did not result to zero.. so I'm now confused. Any help regarding these subjects would be immensely appreciated. Thank you.

 

[Fjolvar]

Here is a copy of my homework. I need help understanding the concepts of number 1.. thank you.

 

[Fjolvar]

I think I may know the answer to one of my questions. If they tell you that a sphere or cylinder has a uniform volume density, then the charge enclosed is not zero. If they tell you there is a uniform surface charge then the charge enclosed is zero?

 

[Bhumble]

My understanding of it anyway...

The charge is only present on the surface of a conducting material. There can still be an electric potential and an electric field inside however.

Yes you are correct about the Q enclosed portion.

The cylinder does not have a zero electric field. The E field is zero when there is symmetry so take just a 2D case of a circle and imagine there is a line charge of uniform density. You would have a zero electric field inside since you have an electric field in opposite directions at each point.
Now imagine that the circle has a length and is in 3D (a hollow cylinder) and centered about the x axis. You would still have symmetry causing there to be a zero E field within the y and z axis of the cylinder but there is no such symmetry along the x-axis where the face of the cylinder is so there would be a field along the x axis.

The other thing you need to be careful about is shells and spheres. With a uniformly charged shell you have an E field of zero inside but you have a non-zero field outside. Now with a sphere, think of it as shells within shells. While each one contributes a net zero E field inside they still all have a non zero field outside their respective radius so the sphere actually has an increasing E field as you move from center until you get to the radius of the sphere.

 

[Fjolvar]

I thought the E field inside a conducting cylinder or hollow cylinder was zero because the charge goes to the surface?

 

[Fjolvar]

I think I figured out most of my questions...

I am however stuck on number 2 on the homework I posted above. I'm assuming we treat the two spheres as a capacitor but in part a the two charges are the same sign and seemingly different charge amounts. So my question is, how does a capacitor behave if the charges are the same sign and thus making it a non capacitor..

How would I go about solving for the surface charge density for inside and outside of the surfaces? Thanks!

 

[Fjolvar]

Anyone?