Eletric field within a cavity of a cylinder.

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To find the electric field within a spherical cavity of radius R/2 inside a uniformly charged cylinder of radius R and length D, Gauss's Law can be applied. The cavity's position, spanning from the concave face to the center of the cylinder, suggests that the symmetry can simplify the calculations. It is hypothesized that the electric field inside the cavity may be zero due to the uniform charge distribution, as the charge inside the cavity balances with the charge outside. The discussion emphasizes the need to clarify the dimensions of the cavity and the cylinder to ensure accurate application of Gauss's Law. Understanding these relationships is crucial for solving the problem effectively.
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Homework Statement


Considering a cylinder of radius, R, and length D with uniform charge density p containing a spherical cavity of radius R/2. Find the field in the cavity.

The cavity sits on one side of the cylinder so that it's diameter spans from the concave face of the cylinder to the center.I'm not sure at what length the cavity is. Probably at D/2. I think that D > R as well.

The Attempt at a Solution


I'm not sure where to start. The only thing that is symmetrical about this problem is that you can cut the shape in half and have two mirror pieces.
 
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I'm thinking that you could use Gauss's Law somehow, but I'm not sure how to apply it. I'm guessing that the field should be zero, as the charge is distributed uniformly and the charge inside the cavity is equal to the charge outside the cavity.
 

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