Purchase Solution

A problem determining capacitance & PD across spherical cap

Not what you're looking for?

Ask Custom Question

Calculate the capacitance of a spherical shell capacitor given two plates one charged at +Q coulombs at a radius (a) from the center another plate charges at -Q coulombs at a radius (b) from the center and given that:

The voltage at a region between the spherical shells is given by

V(r) = kQ/r (a > r > b)

PART A: Write an algebraic expression for the voltage developed between the plates at radii a and b. Your answer will include the parameters Q and a and b

PART B: Using the definition of capacitance derive an expression for the capacitance between the two spherical shells.

PART C: In your expresion for capacitance worked out in PART B work out the value of capacitance given that a = 0.08m, b = 0.10m. Express the answer in proper units.

You may assume an air dielectric

Purchase this Solution

Solution Summary

A problem is posed by the example of a spherical capacitor with plates separated by distance b-a. The problem asks to determine the potential difference seen across the plates of such a capacitor and then goes on to derive an expression for the capacitance of such a device. When given some parameters the solution then goes on to determine the typical numerical capacitance of the said device.

Full linear algebra is developed and a step by step solution provided to show how to tackle such a problem.

Solution Preview

{SEE ATTACHMENT FOR DIAGRAM FIRST}

PART A: Solution.

We are told that the voltage in region between the shells is given by

V(r) = kQ/r (1)

At r = a voltage is therefore

V(a) = kQ/a

At r = b voltage is

V(b) = ...

Purchase this Solution


Free BrainMass Quizzes
Classical Mechanics

This quiz is designed to test and improve your knowledge on Classical Mechanics.

Introduction to Nanotechnology/Nanomaterials

This quiz is for any area of science. Test yourself to see what knowledge of nanotechnology you have. This content will also make you familiar with basic concepts of nanotechnology.

Variables in Science Experiments

How well do you understand variables? Test your knowledge of independent (manipulated), dependent (responding), and controlled variables with this 10 question quiz.

Basic Physics

This quiz will test your knowledge about basic Physics.

The Moon

Test your knowledge of moon phases and movement.