Electric Fields and Gauss' Law

In summary, the electric field of an object is affected by the charge on the surface of the object. The electric 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.
  • #1
Fjolvar
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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 [tex]\rho[/tex] d [tex]\tau[/tex] and [tex]\sigma[/tex] 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.
 
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  • #2
Here is a copy of my homework. I need help understanding the concepts of number 1.. thank you.
 

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  • #3
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?
 
  • #4
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.
 
  • #5
I thought the E field inside a conducting cylinder or hollow cylinder was zero because the charge goes to the surface?
 
  • #6
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!
 
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  • #7
Anyone?
 

What is an electric field?

An electric field is a physical quantity that represents the force exerted on a charged particle by other charged particles in its vicinity. It is a vector quantity, meaning it has both magnitude and direction.

What is Gauss' Law?

Gauss' Law is a fundamental law in electromagnetism that relates the electric flux through a closed surface to the net electric charge enclosed by that surface. It is one of Maxwell's equations and is crucial in understanding electric fields.

How is an electric field calculated?

An electric field can be calculated by dividing the force exerted on a charged particle by its charge. It can also be calculated using Coulomb's Law, which states that the magnitude of the electric field is inversely proportional to the square of the distance between two charged particles.

What is the unit of an electric field?

The unit of an electric field is Newtons per Coulomb (N/C) in SI units. In other systems of units, it can be expressed as volts per meter (V/m).

How is Gauss' Law used in practical applications?

Gauss' Law is used in various practical applications, such as designing electrical circuits, calculating the electric field strength within a capacitor, and analyzing the electric field around conductors. It is also used in the study of electromagnetic radiation and in engineering fields such as electronics and telecommunications.

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