The Electric Field

Purpose: In this lab, we will take a look at the concept of electrical fields. We will also use VPython to show a 3 dimensional representation of an electric field.

Definition of The Electric Field

We start by interpreting the electric field in the same manner as gravity, but we changed some of the words to fit the description of the electric field.

We  know that the electric field is the electrical force divided by the charge the force is exerted on. Therefore, we can make a comparison, where our charge is like mass and the electric field is like the acceleration in Newton's second law.

The Sum of The Electric Fields

On our board, we show a visual representation of all the point charges having an electric fied that converges at a test charge. Like in problems involving gravity, we can use superposition to find the net electric field on a test charge.

On the board, an example of finding the net electric field is displayed. The test charge is to the right of the two charges and on charge is positive while the other is negative.

The next example for solving for the net electric field involves a test charge in between the two opposite charges, a distance above the origin. Using vector analysis, we were able to successfully find the net electric field. The y component cancels while the x component adds in the negative direction.

Using Excel For Computations

On excel, we were able to quickly solve for the net electric field of a rod when we put a test charge next to the end of the rod. the test charge is a distance from the end of the rod.

By inputting the givens in a electric field problem, we were able to solve for the electric field quickly for a problem with changing x and r values. Normally, a problem like this would take much longer by hand, but on excel, we are able to put the necessary equations to solve for the net electric field. This problem was very similar to the previous excel problem except the test charge was in the center of the rod, above the rod. We also had to account for the thickness of the rod, as we were looking at center points in a cylinder.

We take a look at the problem done in the first excel picture, but calculated it without excel. We integrated to find the sum of the electric field. The tricky part was getting the correct limits of integration, as we had to remember that the test charge was not directly next to the end of the rod but a distance away from it.

Electric Field on VPython

On VPython, we set up an axis with a particle of positive charge. We then show the behavior of the electric field using arrows. This was done using Professor Mason's template.

Conclusion:  We see that the electric field of a charge shoots outward or inward radially. We also see that, when finding the net electric field on a test charge, the rule of superposition applys, making calculations fairly simple. We can make comparisons between Newton's second law and the force equation for electric force. We, also, learn that using excel makes calculations faster and easier if done properly.