Gauss' Law and Infinite plane sheet of charge

In summary, the conversation discusses the use of symmetry in calculating the electric field of an infinite plane of charge using Gauss' law. It is mentioned that a cylinder is usually chosen as the Gaussian surface, but other symmetrical shapes such as a cube can also be used. The discussion also touches on the relationship between the electric field and the normal vector on the surface, and the idea that the electric field components perpendicular to the sheet of charge must be cancelled out. Finally, the conversation ends with a request for visual aids to better understand this symmetry property.
  • #1
ximath
36
0
Hi All,

I am studying Gauss' law and have learned that using symmetry, we need to select a cyclinder in order to calculate electric field of an infinite plane sheet of charge.

[tex]2EA = \frac {\sigma A} {\epsilon} [/tex]

That equation is written using Gauss' law and hence E field is found.

However, why wouldn't we use a cube instead of the cyclinder, for instance ?

Moreover, I am not able to understand why the cyclinder is suitable. (I know it is due to the symmetry arguments, but why ? ) I mean, the normal vector on the surface needs to be parallel to E field if we select the cyclinder. However, I can't see why would E field be parallel to the normal vector.
 
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  • #2
Realize that the Gaussian cylinder is oriented so that its flat ends (not its curved surface) are parallel to the sheet of charge.

You are free to use any shape Gaussian surface you wish, as long as you can take advantage of symmetry. For an infinite sheet you can use a cube, cylinder, and many other kinds of surfaces to derive the electric field.
 
  • #3
Hi Doc Al, thanks a lot!

As far as I know I am free to choose any closed surface in fact, however, symmetrical ones are preferable since they help us calculate the electric field.

If I used a cube instead of a cylinder, would it also have the symmetry property ? In other words, on the surface of that plane (which is parallel to the sheet), would electric field and normal vectors be parallel everywhere ? If this is the case, then why would all the textbooks mention about the cylinder but not about a cube as an instance ? One more thing I am trying to realize is why E field is parallel to the normal vector everywhere on the surface that is parallel to the sheet... I think the E field components that are not perpendicular to the sheet must be canceled somehow, but I am having some problems imagining that. Do you have any visual Java applets or even images that explain this symmetry property ?
 
  • #4
ximath said:
As far as I know I am free to choose any closed surface in fact, however, symmetrical ones are preferable since they help us calculate the electric field.
Exactly.

If I used a cube instead of a cylinder, would it also have the symmetry property ? In other words, on the surface of that plane (which is parallel to the sheet), would electric field and normal vectors be parallel everywhere ?
Sure.
If this is the case, then why would all the textbooks mention about the cylinder but not about a cube as an instance ?
Beats me! (Maybe so they can use the same shape for a line of charge.)

One more thing I am trying to realize is why E field is parallel to the normal vector everywhere on the surface that is parallel to the sheet...
If the field did point in some other direction (not perpendicular to the surface) what would determine the direction? The sheet of charge is uniform in all directions, so no one direction can be chosen.
I think the E field components that are not perpendicular to the sheet must be canceled somehow, but I am having some problems imagining that. Do you have any visual Java applets or even images that explain this symmetry property ?
I don't have any off hand, but you might find something if you Google it.
 
  • #5
This thread look to be long dead... however, I did find it useful. I had the same question (more or less) as the OP and post #4 did a good job of explaining things. Thanks Doc Al.
 

What is Gauss' Law?

Gauss' Law is a fundamental law of electromagnetism that relates the electric field passing through a closed surface to the net electric charge enclosed by that surface.

How do you apply Gauss' Law to an infinite plane sheet of charge?

In order to apply Gauss' Law to an infinite plane sheet of charge, you must first choose a Gaussian surface that is perpendicular to the plane. This will simplify the calculation of the electric field, as it will be constant over the entire surface. The net electric charge enclosed by this surface will then determine the electric field passing through it.

What is the formula for Gauss' Law?

The formula for Gauss' Law is E∙A = Q/ε0, where E is the electric field, A is the area of the Gaussian surface, Q is the net electric charge enclosed by the surface, and ε0 is the permittivity of free space.

Can Gauss' Law be applied to any shape or size of charge distribution?

Yes, Gauss' Law can be applied to any shape or size of charge distribution as long as a suitable Gaussian surface is chosen. This means that the electric field may not always be constant, but the overall concept of relating the field to the enclosed charge still applies.

What is the significance of an infinite plane sheet of charge in Gauss' Law?

An infinite plane sheet of charge is often used as a simplified model in Gauss' Law calculations, as it allows for a constant electric field over a chosen Gaussian surface. It is also a useful concept in understanding the behavior of electric fields in real-life scenarios, such as parallel plate capacitors.

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