In this exercise students will calculate the electric potential in the twodimensional region around 1, 2, 3, or 4 small, uniformlycharged spheres. The region is divided into a 25 x 25 grid. The upper left corner of the grid corresponds to x = 0.5 m, y = 0.5 m, and the lower right corner corresponds to x = 24.5 m, y = 24.5 m. The charged spheres can be placed anywhere on the grid. They will be located in the xy plane. Students will calculate the potential at each grid point and construct a surface and a contour plot of the potential.
The potential at r = (x,y,z) outside a uniformly charged sphere centered at r’ = (x’,y’,z’) is
.
In the xy plane we have z = 0 and
.
The constant k has a value of 9*10^{9} in SI units. If we measure q in units of nC = 10^{9 }C, then kq = 9q Nm^{2}/C.
Open a Microsoft Excel spreadsheet.  
Let cells B1  Z1 and cells A2  A26 contain the numbers
0.5  24.5 in increments of 1 as shown below.
Cells B2  Z26 are the grid points whose x and ycoordinates (in units of m) are listed in cells B2  Z2 and cells A2  A26.  
Into cells A31  C34 type the x and
ycoordinates (in units of m) of the positions and the magnitudes (in units
of nC) of four charges. Start with a +10 nC
charge at x = 13 m, y = 13 m and let all the other charges all have zero
magnitude. (Let the x and ycoordinates always be integers. This avoids “divide by zero” errors, since the grid points have
half integer x and ycoordinates.)
 
Now find the potential due to the four
charges at grid point B2.
 
Now copy cell B2 into the other cells of your grid. The grid consists of cells B2  Z26.  
 
Construct another chart of subtype
contour.
You now have a contour plot of the potential outside a uniformly charged sphere. The contour lines are equipotential lines. They are spaced in 5V intervals. (Select a chart style with enough colors.) 
(a) Describe you
graphs. What do they tell you about the potential outside a uniformly
charged sphere? Can you get information about the electric field outside a
uniformly charged sphere from these graphs?
Now change the positions and magnitudes of your
charges. Use
Just type in the new numbers into the cells A31 C34 and the spreadsheet and the graphs will update automatically. 
(b) Describe your graphs. What do they tell you about the potential of this charge distribution?
Again change the positions and magnitudes of your
charges. Use

(c) Describe your graphs. What do they tell you about the potential of this charge distribution?
Again change the positions and magnitudes of your
charges. Use

(d) Describe your graphs. What do they tell you about the potential of this charge distribution?
Again change the positions and magnitudes of your
charges. Use

(e) Describe your graphs. What do they tell you about the potential of this charge distribution?
Pick you own positions and magnitudes for the charges. 
To earn extra credit add your name and email address to your spreadsheet. In full sentences answer the questions (in blue) posed above.
Save your Excel document (your name_exm5.xlsx), go to Blackboard, Assignments, Extra Credit 5, and attach your document.