Electric Potential Video Lessons

Concept

# Problem: A hollow spherical conductor, carrying a net charge +Q, has inner radius r1 and outer radius r2=2r1 (see the figure (Figure 1)). At the center of the sphere is a point charge +Q/2. Plot V as a function of r from r=0 to r=2r2. Assume V0=3Q/8πϵ0r2.

###### FREE Expert Solution

Since r > r2:

$\mathbit{E}\mathbf{=}\frac{\mathbf{\left(}\mathbf{3}\mathbf{Q}}{\mathbf{2}}\mathbf{\right)}}{\mathbf{4}\mathbf{\pi }{\mathbf{\epsilon }}_{\mathbf{0}}{\mathbf{r}}^{\mathbf{2}}}$

We have:

$\begin{array}{rcl}\mathbf{V}& \mathbf{=}& \mathbf{\int }\frac{\mathbf{3}\mathbf{Q}}{\mathbf{8}\mathbf{\pi }{\mathbf{\epsilon }}_{\mathbf{0}}{\mathbf{r}}^{\mathbf{2}}}\mathbf{·}\mathbf{d}\mathbf{r}\\ & \mathbf{=}& \frac{\mathbf{3}\mathbf{Q}}{\mathbf{8}\mathbf{\pi }{\mathbf{\epsilon }}_{\mathbf{0}}\mathbf{r}}\end{array}$

91% (439 ratings)
###### Problem Details

A hollow spherical conductor, carrying a net charge +Q, has inner radius rand outer radius r2=2r1 (see the figure (Figure 1)). At the center of the sphere is a point charge +Q/2. Plot V as a function of r from r=0 to r=2r2. Assume V0=3Q/8πϵ0r2.