Work, Voltage, and Energy relationship

Energy work theorem it is also applied to in the current analyses. As seen in class, work does not depend which path the study object takes to find the amount of work done during that trajectory. It depends just on its initial and final position.

In this picture we have a point charge with various options or possibles directions that can do work. Work is define as the charge that a particular has times the difference in the potential energy or voltage that flow throughout the system. And since the difference in voltage is calculated using the integral because is not the same since a portion is transformed in light, work will be the integral of charge times the electric charge times the distance in which the point charge is moving and the angle it does. From this picture, we can see that the point charge will move in the same direction as the electrical field, but it can move in both directions and produces a negative or positive work. in this case our angle will be 0 degrees, which is A direction.

 As cosine increases the work done on the point charge decreases, which makes sense because it becomes more complicate 'break' the electrical field or the natural flow of the electrical field. As the particle changes its motion tendence and reaches the points D and C, the work is zero because the angle and is zero. Indeed, at this two points, it becomes complicate to move the point charge side way because would require the work to be infinitesimal huge to pass through the electrical field and interrupt the electrical flow. 

This picture simple shows that the electric field moves accordingly with the shape of the surface where the charge is inserted, or where the charge is place. For example the surface can be a cylindrical surface and the electric field will be flown in all directions.