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oreosama
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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 I am 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 I am doing the rest so far right). capacitance isn't given so C = q/v won't help.
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