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## Homework Statement

A cylindrical capacitor of length L consists of a solid conducting core with a radius R and an outer outer hollow conducting tube with an inner radius 3R. A voltage [tex]V_{ab}[/tex] is applied between the two cylinders. Assume L >> R which means we can neglect edge effects.

Given [L, R, [tex]V_{ab}[/tex], K]

Determine:

The charge per unit length for the capicitor

The voltage at 2R

The total charge on the capacitor

The electric field at 2R

the capacitance

the energy stored in the capacitor

Find all answers again if a dielectric K is inserted between the cylinders

## Homework Equations

[tex]\lambda = \frac{q}{L}[/tex]

[tex]\oint E \cdot dA = \frac{q}{\epsilon_0}[/tex]

[tex]V = \int E \cdot dl[/tex]

[tex]C = \frac{q}{V}[/tex]

## The Attempt at a Solution

The question is kind of all over the place and it makes me have doubts on what im doin

[tex]\lambda = \frac{q}{L}[/tex] but we need to solve for q at some point

[tex]V(2R) = \frac{\lambda}{2 \pi \epsilon_0} \cdot \ln{R}[/tex] (use gauss law to solve for E apply to V formula with 3R as "0")

I'm not sure what direction to approach finding the charge(or if im doing the rest so far right). capacitance isnt given so C = q/v wont help.

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