Electric Fields
From MyMCAT
Contents |
Introduction
In the previous section we introduced the concept of charge and how charges produce forces between each other. Here we will take these concepts further to describe the concepts of electric fields.
Electric Fields
The presence of an electric charge produces a force on all other charges present. This "electric force" produces an action-at-a-distance; the charged objects can influence each other without touching. Suppose two charges, q1 and q2, are initially at rest. Coulomb's law allows us to calculate the force exerted by charge q2 on charge q1 (or vice versa). At a certain moment charge q2 is moved closer to charge q1. As a result, the two charges are now closer, and we expect an increase of the force exerted by q2 on q1. . The charges exert a force on one another by means of disturbances that they generate in the space surrounding them. These disturbances are called electric fields. Each electrically charged object generates an electric field which permeates the space around it, and exerts pushes or pulls whenever its electric field comes in contact with other charged objects. The electric field E generated by a set of charges can be measured by putting a point charge q at a given position. The test charge will feel an electric force F. The electric field at the location of the point charge is defined as the force F divided by the charge q:
Just as the force had a magnitude and direction, so does the electric field which is causing the force. By definition, the direction of an electric field is the direction in which a positive charge would move.
Similarly, if we are given a charge and we know that at that position the electric field is of strength E, we can easily determine the force felt on the charge by the following equation:
The Parallels Between Gravity and Electrostatics
An electric field describes how an electric charge affects the region around it. If one has information regarding an electric field then it is possible to determine how a charge will be affected by the electric field. While the concept of an electric field may seem confusing, it is actually already very familiar. Gravity is often discussed in terms of gravitational fields, we just didn't refer to it as a field. When we refer to constant "g", or "the acceleration due to gravity", we are actually referring to the gravitational field produced by the Earth at the Earth's surface!
Consider the expressions for the force of gravity between two masses and the electrostatic force between two charges,
Notice how similar they actually are. As such, the behavior of interacting charges is similar to that of interacting masses, and similar analysis methods can be used. The main difference is that gravitational forces are always attractive, while electrostatic forces can be attractive or repulsive. The charge (q or Q) plays the same role in the electrostatic case that the mass (m or M) plays in the case of the gravity.
A good example of a question involving two interacting masses is dropping a mass m, out a window. The mass m falls because it is interacting with the much larger mass M, the Earth. We often calculate the force on m by using
F = mg
But this is really the same equation as the more complicated equation, GMm/r2, but we have combined G, M, and the radius of the earth squared terms, into a single term g, the gravitational field. (We can do this because at the earths surface none of these terms change.)
So, you've seen a field before, in the form of g. Electric fields operate in a similar way. An equivalent electrostatics problem is to let a charge q be pulled by a uniform electric field E, as we did for m in the Earth's gravitational field g. The force on the charge is given by F = qE, the same way the force on the mass m is given by F = mg. (Thus both "E" and "g" are simplifications of their respective formulas to allow one to calculate the force of the target mass or charge.)
Field Lines
For point charges, the strength of the force can be found by Coloumb's Law. Conceptually however, this does not provide an accurate image of what is going on. Field lines can be used to represent these invisible forces. By convention, lines are drawn in the direction a positive-point charge would accelerate if placed in the electric field. That is, the lines show the force that would be felt. If the source of the field lines was a positive charge, then rays would emanate out of it since any positive charge placed nearby would be repelled away. For a negative charge, any positive charge placed nearby would be attracted to it, and thus field lines converge into it. Graphically, one can observe how the electric field gets stronger as one moves towards the source because field lines become closer and closer. When answering the question, "What direction will the electric field point?", consider that the direction of the electric field will necessarily be tangent to the field line at that point, and thus travel in that direction. If you are adding a collection of charges together, use the vector sum of the electric field at each charge to find the summary electric field at that place. The following equation describes this direction:
Electric Field
Formally, electric field is defined as the force felt by an object, normalized (divided) by the objects charge. If we consider two point charges q1 and q2 separated by a distance r then from Coloumb's law we can calculate the force felt between them.
If we then simplify out the charge of the object we are focusing on, q1, we can determine the electric field coming from this point charge.
Electric fields can also be produced between parallel plates which are charged. In this case and unlike a point charge, the Force felt be a charge between the two plates is the same regardless of the distance it is from either side. Thus, while the force does not change, the equation E = F/q still applies.
