Potential and Continuous Charge Distribution

After talking about charges and electric fields on point particles, we moved on to continuous charge distributions. We began with a uniform ring and a point particle a distance x away. The radius of the ring was a and the ring had a charge of q. Since the distance x from the particle and the radius of the ring make a right triangle, the hypotenuse of the triangle would be the distance between the point particle and the charged ring. In order to find the potential, the charge needs to be known and by plugging it in we can get a result. We also moved the point particle up and added an angle between and solved for the charge as well.

Then we used the previous relationships for solving the potential in order to get to the same result. Using the equation of the integral of the energy field multiplied by the change in distance we came to the same equation of some constant K times the charge over the distance is equal to the potential as well.

Next we moved on to a uniform bar and a point particle an x and y distance away from it. The distance change of course sine the bar is uniform and the distance, unlike a circle, does not remain constant. In this case, we had to replace the change in q with some constant lambda dimes the change in the x direction (y is not needed since that distance does not remain the same). We solved for the x value using Wolfram Alpha and found the potential using the known values. We also went ahead and drew some electric field directions between two equipotential particles.

The day ended after we used a volt meter in order to map out the voltage in respect to the electric fields made by the two "point particles." The set-up is shown below. We were supposed to map the distance and voltage into a table.

The result table is shown below. It is shown that as the distance increases so does the voltage.

The main focus of the class period was to know how charge affects continuous objects and finding problem solving techniques so that we can solve said problems. We also had a visual understanding of electric fields as well as finding electric potential values between each of the charges.