Question

A metal, conducting cylinder of length 0.25 meters contains a total charge of 0.5 coulombs. Use Gauss' Law to find the electric field strength at a radius of 0.1 meters from the cylinder, assuming the cylinder has a radius less than 0.1 meters.

Answer 1

Answer:

Explanation:

Let assume that cylinder has a radius of 0.01 meters. The Gauss Law has the following form:

$\frac{Q_{enc}}{\epsilon_{o}}= E\cdot A$

The electric field considering the cylinder configuration that encloses the conducting cylinder is:

$E = \frac{Q_{enc}}{\epsilon_{o}\cdot (2\cdot \pi \cdot R \cdot L)}$

Where $\epsilon_{o}$ is the absolute permittivity.

$E=\frac{0.5\,C}{\left(8.854\times 10^{-12}\,\frac{C^{2}}{N\cdot m^{2}} \right)\cdot (2\cdot \pi)\cdot (0.011\,m)\cdot (0.25\,m)}$

$E = 3.268\times 10^{12}\,\frac{N}{C}$