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.
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
By the way, if you have covered Gauss's Law, you know all this already.
right?
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.
While both questions involve electric fields and the distribution of charges, they are asking about different scenarios involving different shapes.
In the first question, we have a cylinder with a uniformly distributed charge. The question asks about the electric field outside the cylinder at a distance represented by "r." This means we are considering points that are outside the cylinder but not on its central axis. We need to determine how the electric field strength |E| depends on the distance from the central axis.
To answer this question, we can use Gauss's law. Since the charge is uniformly distributed, the electric field will be spherically symmetric outside the cylinder. We can imagine a Gaussian surface in the shape of a cylinder coaxial with the original cylinder but outside of it. The electric field passing through the Gaussian surface will have the same magnitude at any point on the surface.
Using Gauss's law, we find that the electric field is proportional to the surface charge density (the charge per unit area of the Gaussian surface). For a uniformly charged cylinder, the surface charge density is constant across the surface. Therefore, the electric field is proportional to the inverse of the distance from the central axis (1/r). So, the correct answer is B) |E| ∝ 1/r.
In the second question, we have a uniformly charged sheet. The question asks about the electric field above the center of the sheet at a distance represented by "r." This means we are considering points above the sheet but not exactly on its surface.
To answer this question, we can again use Gauss's law. Since the charge is uniformly distributed and the sheet is infinite, the electric field will be vertically symmetric above the sheet. We can imagine a Gaussian surface in the shape of a cylinder with the center aligned above the center of the sheet. The electric field passing through the cylindrical surface will have the same magnitude at any point on the surface.
Using Gauss's law, we find that the electric field is proportional to the surface charge density (the charge per unit area of the Gaussian surface). For a uniformly charged sheet, the surface charge density is constant across the surface. Therefore, the electric field is independent of the distance from the sheet (r). So, the correct answer is A) |E| does not depend upon r.
While both questions involved electric fields and distributions of charges, the shapes and arrangements of the charges determine the specific behavior of the electric fields in each case.