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. 

       

Voltage, Resistence, and Current.

During this lab, we were analysing how a circuit would be functioning. The picture describes at least four ways that a bulb could be lighted. In all the possibilities, the current flows normally, from the negative to positive, which is the way that must be done so humans can have lighting at home or office. The third scheme, at bottom from left to right, the bulb cannot be lighted because there is not current flow and the the potential difference between the negative side and the positive side cannot be verified. In this case the current will accumulate and there will be an increasing in the temperature. In a home circuit, this temperature rising would, probably, cause a short in the electrical circuit.

This picture gives in a few words how the a simple electrical circuits works, and it is like the one described above. The battery gives energy, the filaments at the bulb will resist to this flow and at same point it will produces light; after passing this resistance, the current will flow back to the battery and the cycle starts all over again. fro this to happen, electrons must flow from one side to another. And for this to a continuous flow, it must have in the circuit a potential difference that is verified when energy tries to pass through the bulb's filament. 

This picture shows that bigger in diameter a wire is, less resistance it will be presented. Lets use an analogous example. When we have a water pipe coming from a water facility treatment plant, it will be divided in various others pipes to reach each of our homes. But lets keep with three just. From the main pipe, we see it that has also two other pipes, one with a bigger diameter than the other one. Water, as humans, will choose the way with least resistance to make the water flow normally and do not cause major problems in the pumps. The same analogy is applied to wire and current flow.

This photo represents a simple circuit where the we have a battery, cables to make the current travel from the positive to the negative pole of the battery. In addition to the lam and battery, a voltmeter and a switch are also included to open or close, making possible that current can flow or not from one side to another. The voltmeter is the controler, like a border, that controls how much is traveling throughout the circuit. 

  

Flux (Continuation)

 Like the last post, in this one we still discussing flux.

  In this photo, students were analysing the lines between three charges and within close, chosen, 'surfaces'. The surfaces that have the point charges within their boundaries will some charge that will go from one point charge to another. It means that they have 'electrons circulating even at the border. Those surfaces are S1, S2, and S3. The Surface S4 has zero flux, because no charge is inside of its boundaries; even though it has a line that passes through, it does not count as as electrical circulation.

In this picture, we had to find a explanation from flux and a mathematical expression that could describe the flux inside of a surface area in a given volume. And since the volume can have any shape, we perform that calculation using integrals. 

This two pictures are describing what happens when a compact disc is putting inside of a micro-have. Lets use water as an example. To heat water, microwave have to 'shoot' electrons that will 'excited' the molecules of water. As the molecules starting get more excited, they will start to gain heat. At a certain point, the molecules will starting to separate from each other, and the water will start to boil. However, with objects like a compact disc, the response is quite different. Until one point it will receive the charges that the microwave will send to heat the disc. But after being saturate with charges, it will re-send it back, or reject, because it cannot expand. At this point the only solution will be 'exploding' to release the excess of electrical charge. The last picture shows what happens when the disc had reached its 'saturation' point. The link bellow shows what we describe it what happens when a compact disc is getting harm on a microwave. 

 What happens with the disc

Electric Flux

In this lab, students were presented with a new concept called Electric Flux (E. F.). E. F. is physically defined as the measure of the number of electric field lines that pass through a surface. One thing that must be said is that EF is always perpendicular to the surface that is been study. 

 This picture represents a prediction that students did of what could be the behavior of a point charge that had been shot and had to pass to an electric field. The prediction was to see where the point charge would go. As the picture shows, the point charge moved to the positive charge, and this movement is described by the moment of Inertia of a particular, which describes how easy or difficult is to a particular move. However, the definition of inertia is that an object tend to remain in constant movement or stopped if there is not external force that change its initial situation. 

In this picture, how to point charges would behave if they were placed in the center of an electric field with some E. F. The conclusion was that the electric field produces a force on each charge, making both of them rotated and keeping the distance between them equal. Since this movement is a rotational movement, the mathematical expression to describe it is Torque (represented with the Greek letter tau) which is described as a force that is applied to an 'object' at certain distance from its point of rotation, And must be always perpendicular to its point of rotation. 

Faraday's Cage

The first picture are just pure calculations in where students could find a mathematical expression to calculate the word done by a point charge. 

The second picture describes how the Flux works on a surface. As explained before, it is always parallel to the surface of the object in study. The video can give us an idea of how this works, even though we do not see the electric field on the Cage. 

Flux Video

In this picture, the intention is to demonstrate that accordentely with the angle between the electric field and the an area enclose withing the direction of the flux. Since the flux is related with the function cosine, it can be said that by increasing the angle between the flux and its direction, we will have less electric field  or lines inside the imaginary 'circuit' created to calculate what can be asked, such as the Flux.