Fourteenth Day

Spring 2015
16th of April's Class

Class started with on of the variants of the concept of Electric's Potential Energy, whose base formula is (kq/r). In the picture above, we were given a ring that possess charge and a point of observation in hovering in the z-axis, away from the center of the ring.

The radius required was modified to (a^2 + x^2) ^0.5. Since the Q, which is the total charge of the ring is 20 microcoulomb, we have to divide it by 20 as there are 20 point charges in the ring. This cause us to have 1 microcoulomb of charge per point.

Calculating the total potential for this system, using the formula of V = [(kq)/(a^2 + x^2) ^0.5)], we also have to multiply it by 20 as there are 20 point charges.

This picture is taken from the Excel spreadsheet, that was made to calculate the same calculation that was done by hand in the previous picture. The spreadsheet calculated the potential from each point of charge, then added them together.

Next, the point of observation was shifted away from the center of the ring. Now it has the x, y and z components of a vector. Using a variation of Pythagoras Theorem, the radius of P2 can be defined by [(x^2) + (y^2) + (z^2)]^0.5. We would then formulate a definition for the radius such that no matter which of the point charges is affecting the observation point, we can still obtain the electric potential, using angle theta and x.

We did the calculation for part (c) of the questions above, and it yielded the results shown in the picture right above this text, which is the same answer as what we obtained previously. In this method, we obtained the formula for electric potential using integration of the formula in the image right below:

In the image below, we derivated the formula for electric potential using a mixture of integration and Pythagoras Theorem's definition for hypothenuse. With this, we have used 3 different ways to derivate for the formula of electric potential.

Next, we deal with electric fields, using the same model for the charged points on a charged ring with the same observation point, as the previous images and questions.

We derivate a way to calculate the x-component of an electric field without relying on angles. We substitute the definition of cos(theta) using Pythagoras Theorem into the original formula.

The area circled in pink is the next part that we were working on. We moved away from the charged ring into a charged rod model. With the given observation point located at (0.1, 0.15), we have to define its electric potential.

With 'a' being the x-component of the observation point, and 'x' is the x-component of the charged point, and 'b' is the y-component of the observation point. We integrate it from 0 (which is the left end of the rod that was treated as an origin) to L (which is the right end of the rod, that describes its length in full).

The last part of class was an experiment we conducted using an electric power supply, multimeter, thumbtacks and a sheet of conducting paper. We were supposed to gauge the electric potential between the two thumbtacks that were pinned to the conductive paper as shown:

Two clips from the electrical power supply would be attached to the thumbtacks. Then we would use the probes from the multimeter to test the potential at both of the thumbacks, and the distance (in 1cm increment) between the two thumbtacks.