ELectric field inside a cavity

[Abhishekdas]

Homework Statement

Suppose there is a cavity inside a metallic conductor...And say a chrge q is placed inside it...Now a charge -q is induced on the inner metal surface and a chrge q appears outside...

Homework Equations

The Attempt at a Solution

Now i have two questions . Firstly i want to know about the charge distribution on the inner and outer sufaces of the metal...Whether it is uniform or not...
Secondly, i know that the field on the inner surface of the metal and along its volume is zero but what about the field inside the cavity(i am talking about the vacuum or air inside the cavity) is that zero too?

I would be really glad if anyone can answer these questions...

 

[luitzen]

Since there are no charges inside the cavity there's no electric flux in a volume only enclosing the cavity and the electric field should be zero.

 

[Abhishekdas]

Flux being 0 means integral E.dS is zero and that makes it clear why field is zero on the inner surface...but i am asking about the space inside the cavity ...field isn't zero throughout the space right?
I mean if you take a point very close to the chrage q then there is going to be some field in that region isn't it?
And can we say anything about the charge distribution being uniform or not?

 

[Abhishekdas]

I am waiting for some more replies...please...

 

[Berko]

There will be a field inside the cavity due to the charge placed inside. The field lines begin (or end) at the charge and end (or begin) at the induced charges on the inside surface of the conductor.

There is no field inside the conductor. However, due to Gauss's law, there is an induced charge on the outer surface of the conductor.

Now, the induced charge on the inside surface is not necessarily uniform. It depends on where the charge is placed inside the cavity. However, the induced charge on the outer surface of the conductor is uniform as there is no "connection" to anything that is happening inside and thus they spread out like they would if you just placed the charge yourself on the conductor and there was no cavity at all.

 

[Abhishekdas]

There will be a field inside the cavity due to the charge placed inside. The field lines begin (or end) at the charge and end (or begin) at the induced charges on the inside surface of the conductor.

There is no field inside the conductor. However, due to Gauss's law, there is an induced charge on the outer surface of the conductor.

Now, the induced charge on the inside surface is not necessarily uniform. It depends on where the charge is placed inside the cavity. However, the induced charge on the outer surface of the conductor is uniform as there is no "connection" to anything that is happening inside and thus they spread out like they would if you just placed the charge yourself on the conductor and there was no cavity at all.

Hey Berko...thanks a lot...your explanations almost perfectly satisfies my queries...But one small thing...You say that the charge distribution on the outer surface is uniform and it has no connection with whatver is inside and i have read this thing in books but no where have they given a proper explanation of why it is independent of the charge inside...So can u give me some proper proof on that?

 

[Berko]

I cannot give you a proof as much as an intuitive argument. The charge on a conductor spreads out due to their mutual repulsion. If there is an electric field present, the charge would then normally change their position due to the field to again reach equilibrium.

But here, there is no electric field felt by the charge on the outer surface so it as if they "do not know" about anything happening inside. Thus, it is no different than just placing charge on a conductor...which spreads out due to mutual repulsion.

 

[Abhishekdas]

Hmmm...you are going by repulsions and i was trying it explain it by thinking that potential has to be same throughout so if there is accumulation of extra charge at some point it violates this and hence doesn't make sense...That is fine it we are talking about a solid conducting sphere with some charge placed on it...(ie with no complications inside)...
But what is this sheilding effect they say...The fact that the conductor sheilds the outer surface from the inner parts and its like as you say they don't know what's going on inside...Why does this happen? I was thinking that had there been an irregular distribution of charge in the inner surface of the cavity then by replulsion it should be irregular outside also...I mean if the inner surface of cavity has a high concentration of positve charge at some area...Then i thought that by induction the part outer surface close to this area should have a high concentration of negative charge...I am just saying this by some vague imagination...i don't know...

 

[Berko]

What induction? There is no electric field connecting them.