Potential difference of concentric spheres

Electricity and Magnetism Level 2

Two charged concentric conducting spherical shells have a potential difference $V$ between them. If the charge of the outer shell is doubled then the potential difference between them will be $\text{\_\_\_\_\_\_\_\_\_\_} .$

V

\frac{V}{2}

The answer will depend on the radius and initial charges.

2V

1 solution

Thomas Welle
Dec 6, 2019

The potential difference between the two spheres is given by:

$V = -\int^{R_2}_{R_1} \vec{E}(\vec{r}) \cdot d\vec{r}$

By Gauss's Law, a uniformly charged sphere creates no electric field inside itself. Therefore, the electric field between $R_1$ and $R_2$ is due only to the inner sphere. So changing the charge on the outer sphere will not affect the field between them, meaning the potential difference will stay the same.

Potential difference of concentric spheres

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