# Faraday's cage

1. Oct 22, 2010

### alphaomega@ho

hello,

I have a very simple question: a hollow sphere has the propertie that in the sphere the electric field, due to being charged , is zero
is it in the whole sphere?
for example, near the inside surface of the sphere, the the electric field of the nearest charge will be geater than the elctric field of the charge wich is a the other side...

another question about this: is the charge always equally divided ?
what about non regular hollow object , is the electric field also zero than (because of its geometry)

thank you very much!

2. Oct 22, 2010

### zhermes

If its a net-uncharged, conducting sphere then yes.

If you are so close to the surface of the sphere that the charge density is no longer uniform, but instead you can "see" individual charges, then no--the field won't be identically zero, but still very close.

Still zero.

3. Oct 23, 2010

### alphaomega@ho

what do you mean with net-uncharged ?
I find it difficult to understand why in a non regular onbject the field whtin is zero
I've seen the disctraction for the a hollow sphere, with those space angle whom causes opposite field vector in this field (reason why the field is zero) => but in a non regular hollow object this isn't true, so whats the reason of havving no netto electric field insie that object?
for example a car...

thank you very mucg

4. Oct 23, 2010

### zhermes

The argument makes no assumption about the particular shape/features of the hollow object except that it is closed, conducting, and uncharged. Think about the inner surface of the conducting object. If there was still a residual electric field there, then electrons on the surface would feel a force and therefore move. Thus the system would not be in equilibrium. The only possible equilibrium configuration, and the lowest energy configuration (thus the preferred configuration), is if there is no electric field at the inner surface.

5. Oct 23, 2010

### alphaomega@ho

so the conclusion:

a hollow object (no matter what shape) with a equally divided charged surface(dq/dA is overall the same) has a electric field inside that has a netto value = 0

thank you very much

6. Oct 23, 2010

### zhermes

Yes, except that $$\frac{dq}{dA}$$ isn't necessarily constant over the surface. I think it will only be constant in the case of zero divergence in the external field, across the surface. Can anyone reading this confirm or deny?

7. Oct 23, 2010

### alphaomega@ho

I mean that dq/dA must be equal over the outer surface
suppose all the charge q is spread out over 1/100 of the outer surface somewhere, in the inside of the object will be an netto electric field
there's no other charge wich creates a internal field opposits to the other dE creates by the other charge on the surface, I think...

what did you mean with zero divergence in the external field ?

8. Oct 26, 2010

### alphaomega@ho

is my statement that I made above correct ?

thank you !

9. Oct 26, 2010

### zhermes

Consider a point-charge located outside the hollow conductor (of arbitrary shape). The induced charge density on the sphere surface will be non-homogeneous, even though the electric field inside the cavity would be zero.

10. Oct 27, 2010

### alphaomega@ho

something like the picture for example?
that I do understand, but for a non homogeneous dq/dA over the outer surface I find it very strange
but I'll except it...

thank you

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