Quick Couple Concept Questions on Guass's Law

[godtripp]

Just a couple quick questions I was wondering about.

Also, this is an Introductory E&M class so we don't actually perform the surface integral

so knowing
$$\oint\vec{E}d\vec{A}=EA=\frac{q_{enclosed}}{\epsilon_{0}}$$

When using cylindrical symmetry I'm supposed to ignore any flux on the top and bottom ends.

Why is this?

Thinking:
$$\oint\vec{E}d\vec{A}= \oint\vec{E}d\vec{A}_{top} + \oint\vec{E}d\vec{A}_{bottom} + \oint\vec{E}d\vec{A}_{side}$$

Can I use guass' law to find the E-field and or flux of a small cylinder or disk?

Lastly, calculating the E field around a sphere some distance away turns out to be the same for an e field of a point charge.
From this the force of the sphere on a point charge would be the same as using coulombs law.

If I have large spheres, would each respective force be the same as using coulombs law (assuming the spheres are not very far away from each other) why or why not?

Thanks!

 

[ehild]

You are right with the cylinders. You should include the top and bottom, but the E field there is different (both magnitude and direction) from the field far from the ends, and it is a difficult problem to find it. The problems given to students usually speak about very long cylinders, so that the area of the ends can be ignored with respect to the side.

As for spheres: If their charge density is fixed and homogeneous, you can handle them as point charges. But you can do this when determining the field outside the sphere. In case of more spheres you can replace them with point charges if you want to determine the field outside of all spheres.

ehild

 

[godtripp]

Thanks a bunch ehild!