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professor190 [17]
3 years ago
5

A cylindrical capacitor is made of two thin-walled concentric cylinders. The inner cylinder has radius 5 mm , and the outer one

a radius 11 mm . The common length of the cylinders is 160 m . What is the potential energy stored in this capacitor when a potential difference 6 V is
Physics
1 answer:
Elden [556K]3 years ago
4 0

Answer:

The  potential energy is PE  = 2.031 *10^{-7} \  J

Explanation:

From the question we are told that

    The inner radius is  r_i =  5 \ mm =  0.005 \ m

      The outer radius is  r_o   =  11 \ mm = 0.011 \ m

     The  common length is  l  = 160 \ m

      The  potential  difference is   V  =  6 \  V

Generally the capacitance of the cylindrical capacitor is mathematically represented as

       C = \frac{2 \pi  *  k  *  \epsilon_o }{ ln \frac{ r_o }{r_i} }  *  l

Where  \epsilon _o is the permitivity of free space with the values \epsilon _o  =  8.85*10^{-12} \  m^{-3} \cdot kg^{-1}\cdot  s^4 \cdot A^2

and  k  is the dielectric constant  of the dielectric material here the  dielectric material is free space so  k  =   1

     Substituting values

             C = \frac{2*  3.142   *  1  *  8.85*10^{-12} }{ ln \frac{ 0.011}{0.005} }  *  160

             C = 1.129 *10^{-8} \ F

The potential energy stored is mathematically represented as

       PE  =  \frac{1}{2} *  C  * V ^2

substituting values

      PE  = 0.5   *   1.129 *10^{-8}  * (6)^2

      PE  = 2.031 *10^{-7} \  J

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