Electric field from concentric spheres

[tony873004]

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 <br /> \frac{{\frac{{r_1^2 }}{{r_2^2 }}}}{{1 + \left( {\frac{{r_1^2 }}{{r_2^2 }}} \right)}}<br /> times the distance between the spheres, closer to the outer sphere.

Is this right? Is this even the way I should express the answer?

 

[Shooting Star]

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

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

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.

The description is wrong.

Is this right? Is this even the way I should express the answer?

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

 

[tony873004]

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 <br /> \overrightarrow E = \frac{Q}{{4\pi r^2 \varepsilon _0 }}{\rm{\hat r}}<br /> ?

 

[Shooting Star]

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

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.

 

[tony873004]

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.

Thanks for your help.