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# A problem determining capacitance & PD across spherical cap

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

#### 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) = ...

#### 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.

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