What Is the Electric Field Inside a Charged Spherical System?

[jaejoon89]

A solid sphere with radius "a" is concentric with a hollow sphere with radius "b", where b > a. If the solid sphere has a charge +Q & the hollow sphere has a charge of -Q, what will be the electric field at radius r, where r < a?

I'm not sure I understand - first of all, is the radius r referring to the distance from the surface of the solid sphere to the hollow sphere?

 

[Defennder]

If I read it properly, r refers to the distance from the centre of the solid sphere with radius a to any point given.

 

[jaejoon89]

Ok, so I guess they are asking for the electric field somewhere inside the solid sphere. This would involve a Gaussian calculation, right? I've got no idea how to model it though...

 

[Defennder]

Yes definitely Gauss law is involved. Except you need to make clear if the solid sphere is a conductor or an insulator. The answers are very different for both.

 

[bchandler]

We're studying the same thing in Physics II...

First, r < a means they want a formula for what the field will be somewhere inside the solid sphere (which itself is inside the hollow sphere).

Firstly, we know that the hollow sphere has no electrical field inside of it, so the hollow sphere can be disregarded.

So, let's consider for a moment that the point we're interested in is somewhere between the center of the solid sphere and the wall of the solid sphere. Now, if you think of the solid sphere as an infinite set of "shells" all stacked up on one another, you know that anything outside of the point can be disregarded, because there is not field inside a uniformly charged shell.

So, at any radius inside the solid sphere, you need to come up with a formula to separate the volume outside of the point from the volume inside of it. Only the volume inside of the point will have an effect on the point. Can you visualize what the new shape of the volume will be? It is itself, a sphere.

So, now we have a point sitting on top of a sphere of uniform charge. What do you know about how a sphere of charge affects a particle that is outside the sphere?

 

[Defennder]

So, at any radius inside the solid sphere, you need to come up with a formula to separate the volume outside of the point from the volume inside of it. Only the volume inside of the point will have an effect on the point. Can you visualize what the new shape of the volume will be? It is itself, a sphere.

So, now we have a point sitting on top of a sphere of uniform charge. What do you know about how a sphere of charge affects a particle that is outside the sphere?

I don't see how that helps. The question as stated by him doesn't say how the charge is distributed on/in the inner solid sphere (nor does it even say if it's a conductor or insulator) So how could you find the E-field for r<a?

 

[bchandler]

I don't see how that helps. The question as stated by him doesn't say how the charge is distributed on/in the inner solid sphere (nor does it even say if it's a conductor or insulator) So how could you find the E-field for r<a?

You're right, I was assuming the sphere was of uniform charge. I am just learning Gauss' law myself, so all I have learned so far are uniform charge distributions, and the question is stated just like all of my uniform distribution problems. In fact, we did that exact same problem in class today (considering the field at a few intermediary points). We at least agree than with uniform distributions what I typed was correct, right?

I also haven't studied how the field is affected by an insulator vs. a conductor yet. In my class so far a "solid sphere" is more like a cloud of point charges which we integrate to get the net field at a point. I just tried to answer based on my knowledge :)