Gauss' Law and Electric Flux

Day 9:  Dipole moments and Electric Flux   

Here we examine the motion of a charged particle in a uniform electric field. We found Fe= qE = ma. When a particle of charge q and mass m is placed in an electric field E, the electric force exerted on the charge is qE. If that is the only force exerted on the particle, it must be the net force, and it causes the particle to accelerate according to the particle under a net force model. 

 The electric dipole moment is defined as the product of the magnitude of charge and the distance of separation between the charges. Here we derived toque(above) which we used to integrate with respect to theta to find work (shown below)

Using the expression for torque which was t=pEsintheta, we plug this into the definition dW=torque*dtheta and integrate it between an angle of θi and θf to find an expression for the work done in rotating the dipole.

here we derived potential energy using a change in energy due to work energy theorem and compared it to gravitational potential energy. 

Here we were given an electric field and we were asked to use Python to predict how the field would look.

Here we have our computer generated electric field. We found that the arrows don't point straight outward but either in or out or side ways, this is because their is a positive and negative charge.

This is where we began our discussion about flux. 

We found that flux is electric field multiplied by area costheta and its units are newtons per coulomb times meters squared.

flux is proportional to charge enclosed over epsilon.

Here we drew an example of how flux would look if it could be seen. Flux is zero when it is parallel to the electric field, and flux is finite when is perpendicular to the electric field.