Question

1. A cylinder has a charge Q placed on it; the charge is distributed uniformly throughout the cylinder. If we examine the electric field E outside of the cylinder, which of the following is true? Assume that r represents the distance from the central axis of the cylinder.
A) |E| ∝ 1/r2
B) |E| ∝ 1/r
C) |E| ∝ r2
D) |E| ∝ r

2. You are examining the electric field of a uniformly charged sheet. If you are a distance r above the center of the sheet, which of the following do you find to be true about the strength of the electric field E?
A) |E| does not depend upon r.
B) |E| ∝ 1/r2
C) |E| ∝ r
D) |E| ∝ 1/r

Wouldn't both questions be the same? I don't know exactly how they're so different aside from the shapes.

Answer 1

for the cylinder 1/r because the E field spreads out as you leave the surface. The same total flux through every 2 pi r. This is only if the length of the cylinder is huge compared to the distance away. If you get far away from a point source cylinder it looks like a point charge and you get the usual 1/r^2
due to 3 dimensional spreading

for the sheet if the sheet is very large compared to r then there is no drop off of E with distance from the sheet. The E lines are all parallel and not spreading out. Of course if the sheet is finite in size and you get far way, it looks like a point source eventually and you once again will get that 1/r^2

Answer 2

By the way, if you have covered Gauss's Law, you know all this already.

Answer 3

right?

Answer 4

Thanks Damon. Couldn't find anything on how it affects different shapes and 3-D figures, but that will most likely be covered the following lecture.