Electric Fields with Calculus Video Lessons

Concept

# Problem: Charge is uniformly distributed with charge density ? inside a very long cylinder of radius R. Find the potential difference between the surface and the axis of the cylinder.

###### FREE Expert Solution

Electric field:

$\overline{)\begin{array}{rcl}\mathbf{E}\mathbf{·}\mathbf{2}\mathbf{\pi }\mathbf{r}\mathbf{l}& {\mathbf{=}}& \frac{\mathbf{\rho }\mathbf{\pi }{\mathbf{r}}^{\mathbf{2}}\mathbf{l}}{{\mathbf{\epsilon }}_{\mathbf{0}}}\\ {\mathbf{E}}& {\mathbf{=}}& \frac{\mathbf{\rho }\mathbf{r}}{\mathbf{2}{\mathbf{\epsilon }}_{\mathbf{0}}}\end{array}}$

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###### Problem Details

Charge is uniformly distributed with charge density ? inside a very long cylinder of radius R. Find the potential difference between the surface and the axis of the cylinder.