Calculating the electric field of a cylinder

In summary, if you have a ring of charge with radius R, the electric field at point X is given by:E= -sigma*R^2
  • #1
Bunnysaur
2
0
I'm trying to calculate the electric field due to a hollow cylinder. The cylinder is "semi infinite" with one end at x=0 and the other at - infinity, and radius R. I'm trying to calculate the field at a point x along the axis (not above the end of the cylinder). The cylinder has charge density sigma (the problem specifically states to use surface charge density instead of line charge).
Am I correct in assuming that the radial field cancels? I can't figure out how to set this problem up.
I'm also supposed to calculate the field at x=0, at the "surface" of cylinder. Is this point inside the cylinder with E =0, or no?

Any help would be much appreciated, thanks!
 
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  • #2
Well, first you are right that the radial force outward from the axis of the cylinder should cancel on the axis of the cylinder. One way to see this is through a basic "symmetry argument." Imagine there were a radial force away from one spot on the axis.

Now imagine we rotated the problem around the axis of the cylinder. The cylinder looks exactly the same, but the radial component is pointing in another direction! We have considered the same problem but gotten different answers about the radial component, so "by symmetry" it must cancel. Another way to see this is that any radial field from one part of the cylinder at a point on the axis would be canceled out by the the radial field from the opposing spot on the cylinder (i.e. the point that is directly across the axis).

Now: how to do this problem? Do you know how to calculate the electric field due to a ring of charge at a point sitting on the axis going perpendicularly through the center of the ring? Use the superposition principle to "build" the cylinder out of infinitely many rings.
 
  • #3
So, I should calculate the field at point X due to a ring of charge with radius R, and then assume that I have infinitely many rings? Wouldn't that just lead to the field being infinite? I'm also under the impression that the closer the charge gets to the center of the ring (the second part of the problem) the larger the field gets, which would also lead to an infinite field.
I've been trying to finish this problem all day, and I'm not convinced that this is the proper way to do it...
 

1. How do you calculate the electric field of a cylinder?

The electric field of a cylinder can be calculated using the formula E = (λ/2πε0)(1/r), where λ is the linear charge density of the cylinder, ε0 is the permittivity of free space, and r is the distance from the center of the cylinder.

2. What is the linear charge density of a cylinder?

The linear charge density of a cylinder is the amount of charge per unit length along the surface of the cylinder. It is typically represented by the symbol λ and is measured in coulombs per meter (C/m).

3. How does the electric field of a cylinder change with distance?

The electric field of a cylinder is inversely proportional to the distance from the center of the cylinder. As the distance increases, the electric field decreases.

4. What is the significance of the permittivity of free space in calculating the electric field of a cylinder?

The permittivity of free space, represented by the symbol ε0, is a constant that represents the ability of a vacuum to store electric charge. It is necessary to include this value in the formula for calculating the electric field of a cylinder as it affects the strength of the electric field.

5. Can the electric field of a cylinder be negative?

Yes, the electric field of a cylinder can be negative. This indicates that the direction of the electric field is opposite to the direction of the positive charge on the cylinder. However, the magnitude of the electric field will always be positive.

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