Electric field

Electric field

The electric field created by a charge is present throughout space at all times, whether or not there is another charge around to feel its effects. The electric field created by a charge penetrates through matter. The field permeates the neighboring space, biding its time until it can affect anything brought into its space of interaction.

The Main Idea

To be exact, the definition of the Electric Field is as follows:

The electric field is a region around a charged particle or object within which a force would be exerted on other objects.

If we put a charged particle at a location and it experiences a force, it would be logical to assume that there is something present that is interacting with the particle. This "virtual force" is in essence the electric field.

A Mathematical Model

The electric field can be expressed mathematically as follows:

[math]\displaystyle{ {\vec{F_{net}} = 0 \Leftrightarrow \frac{d\vec{v}}{dt}} = 0 }[/math]

[math]\displaystyle{ {\vec{F_{2}} = {q_{1}}{\vec{E_{1}}} \Leftrightarrow \frac{d\vec{v}}{dt}} }[/math]

which can be translated to postulate that the force on particle 2 is determined by the charge of particle 2 and the electric field.

Examples

The following examples are to test your basic understanding of the Electric Field. For more examples that test your knowledge of all three of the laws, peruse the class textbook.

Simple

Which way is the electric field going for a negatively charged particle?

It's easy to see that the electric field is pointing toward the negatively charged particle. The electric field is tending toward the negatively charged particle.

Middling

Two charged objects are separated by a distance d. The first charge is larger in magnitude than the second charge.

 A)  The first charge exerts a larger force on the second charge.   B)  The second charge exerts a larger force on the first charge. 

C)  The charges exert forces on each other that are equal in magnitude and opposite in direction. 
D)  The charges exert forces on each other equal in magnitude and pointing in the same direction. 

The answer is of course C, which can be reasoned even by an extension of Newton's Third Law. Using the simple equation in this page, it is also possible to derive and reason this result. Notice that the forces are opposite in direction! The equations above relate vectors, an important concept on physics.

Difficult

Does the object in the following image have a net force of zero? Does it have a constant velocity?

This final example tests your knowledge and understanding of Newton's First Law. We're able to see that the box will accelerate in the -x direction because the net force in the x direction is 5 newtons to the left. However, the box itself has a velocity of 5m/s upwards, which would indeed stay constant. This is because forces (and motion) in perpendicular directions are of each other.

Connectedness

Newton's laws of motion tie into almost everything that we see or do. The first law, in particular, explains why we suddenly lurch forward when a car suddenly stops (our bodies are in a state of motion and thus resist the sudden stop), why it's much harder to stop when ice skating than walking (there's less friction, thus less net force to decelerate), and much, much, more. The importance of Newton's first law (and by extension, the other laws of motion) is not readily apparent, but serves as a basis to explain much of our daily interactions with our surroundings.

It can also apply to things outside of our daily interactions - space, for example. Newton's first law describes why an astronaut in space will continuously float in a direction forever if they are not pulled in by an asteroid or a planet's gravitational force. There is a lack of a net force opposing the astronaut's motion (due to the fact that there is no air in space) which results in the astronaut having a constant velocity. Floating off into space is probably an astronaut's worst nightmare, a scenario that a recent movie, Gravity, explored. The entire premise of the movie (Sandra Bullock becomes untethered from her space station) relies on Newton's first law of motion.

History

While Galileo is the one credited with the idea of inertia motion, it was René Descartes, a French philosopher, who would expand upon Galileo's ideas. Descartes went on to propose three fundamental laws of nature in his book, Principles of Philosophy, the first of which stated that "each thing, as far as is in its power, always remains in the same state; and that consequently, when it is once moved, it always continues to move." Thus, while the concept of inertia is often referred to as Newton's First Law, it was first described by Galileo and then perfected by Descartes decades before Newton published his findings.

As for Newton, he first described his three laws of motion in The Mathematical Principle of Natural Philosophy, for the Principia, which was published in 1687. These laws described the relationship between an object and the forces acting upon it and laid the foundation for classical mechanics. While Newton's first law came from the work of Descartes and Galileo, his other laws are the work of himself.