A capacitor is formed from two concentric spherical conducting shells separated by vacuum. The...

Question:

A capacitor is formed from two concentric spherical conducting shells separated by vacuum. The inner sphere has radius {eq}11.0 \ cm, {/eq} and the outer sphere has radius {eq}14.5 \ cm. {/eq} A potential difference of {eq}140 \ V {/eq} is applied to the capacitor.
(a) What is the energy density at {eq}r = 11.1 \ cm, {/eq} just outside the inner sphere?
(b) What is the energy at {eq}r = 14.4 \ cm {/eq}, just inside the outer sphere ?

Cylindrical Capacitor - Energy Density

Cylindrical capacitor consists of two concentric metallic conductor separated by vacuum or some dielectric medium. The electric field exists between the capacitor plates {eq}E = \dfrac { \lambda } { 2 \pi \epsilon_0 r } {/eq}. Here {eq}\lambda, \ \ \epsilon_0, \ \ r {/eq} are the linear charge density on the inner conductor, permittivity of free space, distance from the center of the inner sphere to the point where field is evaluated between the cylinders. The electric potential difference between the cylinders {eq}V = \dfrac { \lambda } { 2 \pi \epsilon_0 } \ln ( \dfrac { b } { a } ) {/eq}. The terms a and b are the inner cylinder radius and outer cylinder radius respectively. The electric field energy density in the electric field {eq}U_e = \dfrac { 1 } { 2 } \epsilon_0 E^2 {/eq}

Answer and Explanation:

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Given points

  • Radius of the inner sphere a = 0.11 m
  • Radius of the outer sphere b = 0.145 m
  • Potential difference between the cylinders V = 140 V
  • Permi...

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Calculating Electric Forces, Fields & Potential

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Chapter 7 / Lesson 6
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From electric charges come electric forces and electric fields. In this lesson, we will explore how to calculate electric forces between charges, electric fields generated by them, and electric potentials in specific locations because of them.


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