# Electric field from concentric spheres

1. ### tony873004

1,587
Two concentric spherical surfaces with radii R1 , R2 each carry a total charge Q. What is the electric field between the two shells?

I don't know what kind of answer they are expecting. Do I just describe it? Here's my attempt:

The field lines from the inner shell will point away from the inner shell towards the outer shell. The field lines from the outer shell will point away from the outer shell towards the inner shell. Since the outer shell has the same total charge as the inner shell, but it is spread out more over the larger surface area, the point where the field lines meet will be closer to the outer shell.

$$\frac{{4\pi r_1^2 }}{{4\pi r_2^2 }} = \frac{{r_1^2 }}{{r_2^2 }}$$
So the field lines from the inner sphere will be $$\frac{{r_1^2 }}{{r_2^2 }}$$
stronger than from the outer sphere. So the distance is $$\frac{{\frac{{r_1^2 }}{{r_2^2 }}}}{{1 + \left( {\frac{{r_1^2 }}{{r_2^2 }}} \right)}}$$ times the distance between the spheres, closer to the outer sphere.

Is this right? Is this even the way I should express the answer?
1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution
1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

2. ### Shooting Star

1,979
The field or the electrical intensity is a mathematical quantity, a vector in fact, and should be written as such.

The description is wrong.

Not right, and no, you should express your answer mathematically. Read up on Gauss' law and fields due to charged shells.

3. ### tony873004

1,587
Thanks, Shooting star.

Reading up on it, it seems that there are no field lines inside a shell. So would that mean that the outer shell can simply be ignored? Is the answer simply $$\overrightarrow E = \frac{Q}{{4\pi r^2 \varepsilon _0 }}{\rm{\hat r}}$$ ?

4. ### Shooting Star

1,979
This was the original framing of the problem. Here, we have tacitly assumed (and the problem-maker probably implied) that the surface charge density on the shells are uniform. In that case, the expression you have given is correct.

On the other hand, in the problem it is only mentioned that the the total charge is Q on each surface. If it is not uniformly distributed on each surface, then there is no general formula to describe the field.

5. ### tony873004

1,587
It wouldn't be the first time this book expected me to assume something. This problem reminds me of the gravity analog. If all Earth's mass were concentrated in a shell with Earth's diameter, gravity would be 1g on the outside surface and 0 everywhere inside.