Electric Potential

He we showed multiple ways to derive electric potential and an observation location, point P. First we do it when P is at a distance X from the center of the ring, then we move P to a distance of X from the top of the ring. We knew that V = kq/r so with this we found dV = kdq/r, and in this situation r is equal to sqr(x^2 + a^2). For the second point we found that cos(theta) was equal to x/r and with this we determined that V = cos(theta)kq/x.

The above picture shows how we calculated the electric potential yet another way, with the equation shown on the left, integral from a to x of E(electric field) dot change in position (ds). E is only from the x component in this so we take Ex to equal kq/r * cos(theta) (r is equal to sqr(x^2+a^2) and we use cos(theta) since we only care about the x value in this). We see yet again that the potential is equal to kq/sqr(x^2+a^2).

 

We worked out what the net electric potential was from a rod to an observation point which was 15 cm above it.

In this excel file we first found the Vnet when there were 20 segments on a ring given the x and a values (x is the distance from the ring and a is the radius of the ring). R, the radius, is the square root of the sum of x squared and a squared. dQ was just the given q divided by 20. To find dV we multiplied the k and dq values and divided by R, then we multiplied by 20 to find Vnet of the ring. The second part of the excel file shows the net Q value and dV values from an observation point that was 15 cm away from a rod. The Y value is the same in each case but the X values varied.

For this lab we used a multimeter to find the difference in potential from a negative charge (ground) to another spot on the black conductive paper. We used a voltage regulator to set the potential of the positive and negative pins at 15 Volts. Harrison placed the black pin on the ground thumbtack and used the red pin on various points on the paper and Mario read the measurements while I recorded. We repeated this process 9 times to the left of the ground pin and 6 times to the right of the ground pin. In the lab book we calculated Work with the equation W = Vq.