🤓 Based on our data, we think this question is relevant for Professor Pantziris' class at UTAH.

For a very long uniformly charged cylinder with a radius R and a linear charge density λ, the volume charge density, ρ, for the length of the cylinder would be expressed as:

$\overline{){\mathbf{\rho}}{\mathbf{=}}\frac{\mathbf{q}}{\mathbf{\pi}{\mathbf{R}}^{\mathbf{2}}\mathbf{L}}}$, where q is the charge on length, L.

The linear charge density, λ:

$\overline{)\begin{array}{rcl}{\mathbf{\lambda}}& {\mathbf{=}}& \frac{\mathbf{q}}{\mathbf{L}}\\ {\mathbf{\rho}}& {\mathbf{=}}& \frac{\mathbf{\lambda}}{\mathbf{\pi}{\mathbf{R}}^{\mathbf{2}}}\end{array}}$

Electric flux:

$\overline{){{\mathbf{\varphi}}}_{{\mathbf{E}}}{\mathbf{=}}{\mathbf{\int}}{\mathbf{E}}{\mathbf{.}}{\mathbf{d}}{\mathbf{A}}}$

Remember A•B = ABcosθ

**a.**

Electric flux from the Gaussian surface is:

$\begin{array}{rcl}{\mathbf{\varphi}}_{\mathbf{E}}& \mathbf{=}& {\mathbf{\int}}_{\mathbf{c}\mathbf{u}\mathbf{r}\mathbf{v}\mathbf{e}\mathbf{d}}\mathbf{E}\mathbf{d}\mathbf{A}\mathbf{c}\mathbf{o}\mathbf{s}\mathbf{(}\mathbf{0}\mathbf{\xb0}\mathbf{)}\mathbf{+}\mathbf{2}{\mathbf{\int}}_{\mathbf{p}\mathbf{l}\mathbf{a}\mathbf{n}\mathbf{e}}\mathbf{E}\mathbf{d}\mathbf{A}\mathbf{c}\mathbf{o}\mathbf{s}\mathbf{(}\mathbf{90}\mathbf{\xb0}\mathbf{)}\\ & \mathbf{=}& \mathbf{E}\mathbf{\left(}\mathbf{2}\mathbf{\pi}\mathbf{r}\mathbf{l}\mathbf{\right)}\mathbf{+}\mathbf{0}\end{array}$

A very long, uniformly charged cylinder has radius R and linear charge density λ.

a. Find the cylinder's electric field strength outside the cylinder, r ≥ R. Give your answer as a multiple of λ/ε0.

Express your answer in terms of some or all of the variables R, r, and the constant π.

b. Find the cylinder's electric field strength inside the cylinder, r ≤ R. Give your answer as a multiple of λ/ε0.

Express your answer in terms of some or all of the variables R, r, and the constant π.

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What scientific concept do you need to know in order to solve this problem?

Our tutors have indicated that to solve this problem you will need to apply the Gauss' Law concept. You can view video lessons to learn Gauss' Law. Or if you need more Gauss' Law practice, you can also practice Gauss' Law practice problems.

What professor is this problem relevant for?

Based on our data, we think this problem is relevant for Professor Pantziris' class at UTAH.