Electric Fields: flux, torque

Lab Day 10: 3/26/15 Electric Fields, torque, and Flux

Purpose:The purpose of today's experiments were to analyze the idea of torque and flux when applied to electric fields. 

Electric Dipole, Torque

The electric dipole moment is the product of the magnitude of the charges and the separation between two charges and is directed from the negative charge to the positive charge. The net force on the dipole is zero. We can apply torque on this concept in our electric field. , the torque is defined as the R vector cross the F vector and  there with torque on both charges there is a clockwise rotation. To find the torque in terms of q,E,theta, and A, the force is Eq, while the dipole vector would be 2Aq. By substituting these terms, we come up with the torque as the dipole vector cross the electric field vector.

Work, Potential Energy(enclosed)

The work is shown in relationship to torque where we derived the equation of work in terms of a rotation. Using the expression found for torque, we were able to find the work done in rotating the dipole due to the work energy theorem.

We went further to find the potential energy enclosed which is just the dot product of the electric dipole moment with the electric field. 

3-D modeling of Electric Field vectors and Arrow positions

In this activity, we used the Vpython modeling program to look at the electric field vectors in 3-D where we learned to program the electric field vectors to point in specific axis. The whiteboard above shows the predicted model where the arrows all point toward the positive x-axis. However in reality, the arrows all point toward different positions due to the two point charges as seen in the screenshot view of the model.

The electric field lines are useful in showing a continuous way to show the density of the electric field caused by point charges.In our drawing we have a positive particle and a negative particle and the field lines are drawn going toward the negative particle where we can observe how the more closely packed lines (more dense) represents areas with higher electric field strength.

Flux Model

The nail bed is an example of a flux model. The nails are normal to the wooden surface and we can see that each nail can be observed as electric field vectors. When Prof. mason used a wire, he captures as much vectors as the rectangular wire allows it. It is seen that the maximum flux is obtained when the angle between the area vector and electric field vector is zero. When the wire is tilted, there is less electric field vectors and as it gradually goes to 90 degrees, since there is less electric field vectors, there would be less flux as well. Therefore, we can use the idealized model of 

flux to calculate the flux in relationship to the electric field.

We can identify flux as the number of electric field lines passing through a given surface. The flux going in where the electric field vector and the change in area is parallel allows us to find that flux is equal to the electric field vector dot the area. The model below of a cube shows that flux is present (green surface) when the normal vector is parallel to the electric field vectors, while the flux is zero (red surfaces) when the normal vector is perpendicular to the electric field vector.