I need help on this:
The Laplace equation for electrostatics is 2V=0. This is easily solved for simple cases such as the parallel plate capacitor. For more involved situations, numerical methods are usually required. To give you some insight into numerical solutions, lets use a spreadsheet (such as Excel) to solve the Laplace equation in cartesian coordinates.
For the voltage, Vi at the point xi, a simple approximation for the derivative is
and the second derivative is obtained from the first as
(i) Take the case of a parallel plate capacitor with 5V across it. Set up a spreadsheet to solve for the voltage from the grounded plate to the 5V plate. Plot V versus x to ensure the solution is correct.
(ii) Extending this to 2 dimensions (x,y) and setting Δx=Δy=h then
Using the spreadsheet, compute the voltage inside a long conducting box (in the z direction) with square cross section (in the x-y plane) that has one side at 5V and the rest at zero volts.
2006-10-02
04:41:17
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1 answers
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asked by
bye_1981
1
in
Physics