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DaniilM [7]
3 years ago
5

A capacitor consists of two concentric cylinders. The inner cylinder has a radius of 0.001 m and the outer cylinder a radius of

0.0011 m. The length of the capacitor is 1 m. If centered on the z-axis, the region 0 < ∅ < π has a dielectric constant of 2 and the region π < ∅ < 2π a dielectric constant of 4. Find the capacitance. Ignore fringing fields.
Physics
1 answer:
AlexFokin [52]3 years ago
5 0

Answer:

The capacitance is 1.75 nF

Explanation:

From the question we are given that

    The inner radius is r_{in}  = 0.001

     The outer radius is r_{out} = 0.0011 \ m

    Length of the capacitor is L = 1m

    The dielectric constant is Di = 2 \ for  \ 0 < \phi < \pi

   The dielectric constant is  Di_2  = 4 \ for \ \pi < \phi < 2\pi

Generally the capacitance of a capacitor can be mathematically represented as

                C = \frac{\pi \epsilon_0 Di_1 L}{ln\frac{r_{out}}{r_{in}} } + \frac{\pi \epsilon_0 Di_2L}{ln\frac{r_{out}}{r_{in}} }

                   = \frac{\pi \epsilon_0 L (Di_1 + Di_2)}{ln\frac{r_{out}}{r_{in}} }

                  = \frac{(3.142)(8.85*10^{-12})(1)(2+4)}{ln\frac{0.0011}{0.001} }

                  =1.75*10^{-9} F

                  1.75nF

                 

                   

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