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Worksheet 7

**PHY201, 2000**

Donev Aleksandar

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Electrostatic potential of a system of charges

This problem is quite interesting and can be solved in many ways, some efficient and well-structured, others quick and sloppy. I will follow the recommendations given in the assignment, which make this look similar to the corresponding Fortran 90 code.

First we choose positions for the 4 charges and their magnitudes, and enter them as matrices (nested lists in *Mathematica*):

The electrostatic potential at a given point with position *R* is simply the sum of the potentials from the four individual charges. Each of the individual forces is given with U(R)=. I define the potential as a function of the position *R* where the potential is measured, using the standard *Mathematica* constructor:

*Function[x_]:=Expression with x*

Just to make sure there are no numerical singularities, we add a small number to the denominator:

Now we can plot this function by setting *R={x,y}*:

Notice that the potential becomes singular near the four charges, but is otherwise fairly smooth in-between. So it is probably better to plot the coutours of the potential surface:

And here is the electric field:

Converted by *Mathematica*
December 12, 2000