I am not submitting this as my own work, I simply need help answering some questions
You work in a company that designs and builds pollution control devices. One such device is an electrostatic scrubber. To achieve the necessary electric potential requires complex electrode shapes. The computer simulation to determine this shape builds the electrode potential by approximating it as a collection of millions of point charges and adding the effect from those point charges. To speed up the design process you wonder what would be the fewest number of point charges that give you a good enough approx. of a rod's potential. To explore this idea, you decide to calculate the electric potential at a point a short distance from a charged rod along a perpendicular to its axis that is through the middle of the rod, and also at a point a short distance from the end of the rod along its axis. You then compare these results with those obtained using the computer simulation using different numbers of charges to simulate a charged rod.
1) Make a picture of the situation where you want to determine the potential of a charged rod outside of the rod along an axis through it.
2) make an expression for the part of the electric field at the point of interest that is caused by a single point charge of the many that are distributed in the rod.
3) Describe how the part of the potential at your point of interest, that is caused by a single point charge is related to part of electric field at that point.
4) There are now several ways to determine the potential at the point of interest. 1) You could add all the parts of the potential from every point charge making up the bar or
2) you could add all the parts of the electric field from every point charge making up the bar and then use that electric field to get the potential at the point of interest. Describe how you would use each of these methods and discuss their pros and cons.
5) There is another method that might solve this problem. You could try to use Gauss' law to determine the electric field at the point of interest. Then use that electric field to determine the potential at that point. Then use that electric field to determine the potential at that point. Discuss whether or not this would be a useful approach. If it is describe the Gaussian surface that you would use. If not, describe why Gauss' Law is not useful for this application.