# Charge distribution over two thin concentric spherical shells

• captainjack2000
In summary, there are two conducting spherical shells, one with a charge q and the other with a net charge Q, and they are concentric with each other. The charge is distributed between the inner and outer surfaces of the shells, with +q on the outer surface of the inner shell, -q on the inner surface of the outer shell, and +Q-q on the outer surface of the outer shell due to induced charge. The capacitance of the two shells can be calculated using the equation C=Q/V, where Q is the net charge and V is the potential. To be a capacitor, the two plates must have equal and opposite charges. Gauss' law can be used to calculate the electric field and then determine the capacitance

## Homework Statement

"A thin conducting spherical shell of radius a carries a charge q. Concentric with this is another spherical shell of radius b>a carrying a net charge Q. Describe how the charge is distributed between the inner and outer surfaces of the shells. What is te capacitance of the two shells?"

## The Attempt at a Solution

Is it correct to say that there would be a charge +q on the outer surface of the inner shell. Due to induced charge there would then be a charge -q on the inner surface of the outer shell. Therefore there would be a charge +Q-q on the outer surface of the outer shell.

For the capacitance does it want the capacitance of the overall system. C=Q/V ??

Q is the net charge, when i did this question i took it to mean that Q=-q as it is induced by the +q on the inner sphere. note: to be a capacitor the two plates have to carry equal and opposite charges.

use gauss' law to get the field and then go from there in order to get the capacitance.

+Q-q ?

## 1. How is charge distributed over two thin concentric spherical shells?

The charge on each shell is distributed uniformly, with an equal amount of charge on each infinitesimal element of the surface.

## 2. What is the total charge on each shell?

The total charge on each shell is equal to the product of the surface area and the surface charge density.

## 3. How does the charge distribution change if the shells have different radii?

If the inner and outer shells have different radii, the charge distribution will be different. The smaller shell will have a higher surface charge density, resulting in a stronger electric field near its surface.

## 4. How does the charge distribution change if the shells have different charge densities?

If the two shells have different charge densities, the charge distribution will also be different. The shell with the higher charge density will have a stronger electric field near its surface.

## 5. Can the charge distribution over two thin concentric spherical shells be described by a mathematical formula?

Yes, the charge distribution can be described by the mathematical formula Q = 4πε0σr2, where Q is the total charge, ε0 is the permittivity of free space, σ is the surface charge density, and r is the radius of the shell.