The electric potential of 2 hollow concentric spherical shells

[Figigaly]

Homework Statement

Consider two concentric conductive hollow spherical shells. The inner shell has radius R1 and holds the charge +q. The outer shell has charge R2 and holds charge -q. Determine an expression for the potential difference between the shells.

Homework Equations

V = q / (4 pi ε₀ r) when r greater or equal to the radius of the shell

V = q / (4 pi ε₀ R) when r is less than the radius (R) of the shell

The Attempt at a Solution

I said due to fact that electric potential has superposition principle. The total electric potential between the shells:
therefore: V = q / (4 pi ε₀) (1/r - 1/R2)
I am unsure if this is true or not any help would be appreciated, Thanks

 

[ideasrule]

Yup, looks right to me.

 

[kerimek]

Your solution is correct. The total electric potential between the shells can be calculated using the superposition principle, which states that the total potential at a point is the sum of the potentials due to each individual charge. In this case, the inner shell with charge +q and the outer shell with charge -q contribute to the total potential between the shells.

Using the equation V = q / (4 pi ε0 r) for r greater or equal to the radius of the shell, we can calculate the potential due to the inner shell at any point between the shells. Similarly, using the equation V = q / (4 pi ε0 R) for r less than the radius of the shell, we can calculate the potential due to the outer shell at any point between the shells.

Therefore, the total potential between the shells is given by the sum of these two potentials, which is V = q / (4 pi ε0) (1/r - 1/R2). This expression is valid for any point between the shells, including at the surface of the inner shell (r = R1) and the surface of the outer shell (r = R2).