# How exactly do we know the direction of the E-field here?

## Homework Statement

http://plato.stvincent.edu/physics/past/ph112/2008/exam1/s3.pdf [Broken]

How do we know the E-field is radially? And not through the top and bottom?

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gneill
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How do we know the E-field is radially? And not through the top and bottom?
Symmetry. Without an imposed coordinate system, how would you distinguish a "top" from a "bottom"?

Symmetry. Without an imposed coordinate system, how would you distinguish a "top" from a "bottom"?
The circular top and bottom.

Like why isn't it

[PLAIN]http://img171.imageshack.us/img171/9951/39044375.jpg [Broken]

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gneill
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The problem statement says that it is a "long cylindrical charge distribution ... of which a segment is shown". The end caps can be considered to be distant from the segment under consideration.

It's much like the uniform field assumption for the parallel plate capacitor, where the edge effects are taken to be negligible compared to the majority of the plate surface area.

If you're asking why the electric field lines don't spontaneously decide to bunch together into a tube shape and only run parallel to the cylinder, then take it as a property of space that it tries to "dilute" flux density -- it's as if the flux lines are mutually repellent, so they naturally arrange themselves into the minimum energy density state which is radial divergence.

I haven't learned what a capacitor is yet....

I still haven't even learned voltage yet

When they mean "long" it is a disguised way of saying "infinity" right?

gneill
Mentor
I haven't learned what a capacitor is yet....

I still haven't even learned voltage yet

When they mean "long" it is a disguised way of saying "infinity" right?
Well, let's just say that it's a strong hint that you can take the length to be great enough that no "edge effects" need be considered, and that everything under consideration will be well behaved in the area that you're concerned about!

Basically in electrostatics the field lines are orthogonal to the charged surface !

Remember it ;)

** There is an explanation for this of course, try to ask your teacher why they are perpendicular to the surface.

## Homework Statement

http://plato.stvincent.edu/physics/past/ph112/2008/exam1/s3.pdf [Broken]

How do we know the E-field is radially? And not through the top and bottom?
Your intuition is correct, the field lines are only radial in the center of the cylinder without an axial component.

It's supposed to be an idealized cylinder as you are given the statement "Consider a long cylindrical". In other words r<<L. But there will still be electric field lines from the ends.

By the way your drawing is incorrect. You should have the electric field existing both ends, or entering, depending upon the sign of the charge.

By the way, your drawing is incorrect, in the real world you will have field lines exiting both ends (or entering, depending on whether it is charged positive or negative).

The problem set-up is poorly worded. We are given that R>>r. We must also assume L>>R and examine the field lines near the center (more oversights) where we don't have to deal with end effects from the finite length of L.

It would have been better to have said that the length was infinite, and be done with it.

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