Solving Infinite Cylinder Homework w/ Electric Field Inside Void

In summary, the problem is to prove that the electric field inside an infinitely large cylindrical void in an infinitely large evenly charged dielectric cylinder is homogeneous and to find its value. This can be done by using Gauss's law to calculate the field at any point in the uniformly charged cylinder and then adding the fields of two additional cylinders of opposite charge densities.
  • #1
funoras
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Homework Statement


In an infinitely large evenly charged dielectric cylinder(charge density is [itex]\rho[/itex] ) there is an infinitely large cylindrical void. Prove that the electric field inside the void is homogenous and find its value. (picture)
http://img513.imageshack.us/img513/5747/61734727.png

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Homework Equations


The Attempt at a Solution


I don't think i can use Gauss law here. Any ideas ?
 
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  • #2
You can calculate the field at any point (radius) in a uniformly charged cylinder using Gauss's law. Now add 2 cylinders, one big and one small, of opposite charge densities to create the hole. The field within is the sum of the fields within each cylinder.
 

1. What is an infinite cylinder?

An infinite cylinder is a theoretical object with no end or edge, extending infinitely in all directions. It has a uniform shape and can be described by its radius and length.

2. What is "electric field inside void"?

"Electric field inside void" refers to the electric field that exists within an empty space or void inside the infinite cylinder. This term is often used in physics problems to describe the electric field in a specific region of space.

3. How do you solve for the electric field inside a void in an infinite cylinder?

To solve for the electric field inside a void in an infinite cylinder, you can use the Gauss's law, which states that the electric field at a point is equal to the charge enclosed by a surface surrounding that point divided by the permittivity of the medium. In this case, the enclosed charge would be the charge of the infinite cylinder outside the void.

4. What factors affect the electric field inside the void of an infinite cylinder?

The electric field inside the void of an infinite cylinder is affected by the charge of the cylinder, the distance from the center of the cylinder to the void, and the permittivity of the medium. It is also affected by any other charges or conductors present in the surrounding space.

5. Can the electric field inside the void of an infinite cylinder ever be zero?

Yes, the electric field inside the void of an infinite cylinder can be zero if the charge of the cylinder is evenly distributed and the distance from the center of the cylinder to the void is large enough. In this case, the electric field would be cancelled out by the electric field of the surrounding charges.

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