Electric Field!

Lab Day 9: 3/24/15 Electric Fields

Purpose: The purpose of today's experiment was designed to focus on the electric field. The electric field can be derived from coulumbs law. We were able to utilize vpython to analyze the forces and arrows in an electric field looking at a point particle in three dimensions.

Experiment:

We began class by relating the gravitational force with electric field and calculated electric field below using electrical force and electric field equations.

Next, we used trigonometry to define our constants and determine our unit vector quantities of electric field. The electric field can be defined using a given point charge at a particular distance away.

Here are calculations of the net electric field which is just the sum of all the electric field vectors that we derived above. We were able to determine this by identifying the direction of the force and finding the distance between each particle that is causing it to attract/repel.

When a point particle is not designed in a straight line the electric field can be derived using the x and y components as shown in the calculations below. In fact when we take the limit of the electric field, we find that it is zero.

3-D Modeling of Electric Fields

Next, our group made predictions of the program of the electric field that was designed and it consisted of a point particle with three axis cylindrical in shape. 

Predictions of Vpython model program

By using Vpython modeling program, we produced the predicted electric field. Initially the arrows were pointing in the same direction toward the positive x-axis. We converted it, by auto scaling for each of the six vectors inserting as seen in the screenshots below to produce the correct position for the arrow vector.

Superposition Electric Field Vectors

Excel calculations a rod divided by 10 parts.
Find the electric field on the rod.

In this activity, we looked at the electric field calculations along the axis of a rod. We further analyzed a rod with 10 increments which allows us to determine the electric field in x and y components which can be calculated in excel for each of the 10 parts. Using superposition, we can derive vectors in order to find the net electric field in different components. The calculations from the white board allowed us to create multiple variables to find the net electric field in excel. The electric field was found and by using the proportionality of the components we found the x and y electric field vectors.

Excel Calculations of Electric Field Components

Calculations of Electric field

Electric Field due to a differential Charge Symbolic Calculations

In this part, we took the integral of the electric field using the line charge density where dq=(lamda)dx to find the equation that relates to the magnitude of the electric field.