# Electric Fields

An electric field is a non-contact force (like gravity or magnetism). The
British Physicist Michael Faraday developed the concept by considering a
point charge permeating lines of electric field in every direction in space. When another point is brought near it (and we use a very small positive point charge as a "test"
charge) the point feels a field. This gives an **electric field, E**, defined as:

where **F** is the Force exerted on the charge and q is the
magnitude of the charge. Our units are force per unit charge, or Newtons/Coulomb. Electric field has both magnitude and direction so it is a vector quantity.

We can do some more manipulations with this formula. Recall Coulomb's Law (
F = kq_{1}q_{2}/r^{2}). If we combine this and the definition of Electric field, we get

and the test charge value (q) cancels out, so

Note that if Q is positive, it repels the test charge and the field lines are directed out from the point charge. If Q is a negative charge, then the field lines are directed toward the point charge.

k can also be expressed in terms of the permittivity of free space,
**e**_{o}. k = 1/4**pe**_{o}^{,} or

Here is a quick example:

1. *Calculate the magnitude and direction of the electric field at point
P which is 50 cm to the right of a point charge Q = - 5.0 x 10 ^{-6} C.*

Answer: From the picture, we see our positive test charge on the left and our point charge Q on the right. Since the charge is negative, the field points to bring the charges together. The magnitude of the field is given by:

E = kQ/r^{2}_{,} or (9 x 10 ^{9} N
m^{2}/C^{2})(5.0 x 10^{-6}C)/(.50m)^{2} = 1.8 x 10 ^{5} N/C

If multiple charges or test points are available, the problem is solved by finding the field at each point from an individual charge and then adding the fields using vectors, as shown below:

Q_{1} and Q_{2} both represent negative charges of some
magnitude. E_{1} and E_{2} represent the individual fields felt by point *P* from Q_{1} and Q_{2} respectively. The vector at **E** represents the
total electric field felt at point *P* and is the vector summation of E_{1} and E_{2}. This is known as the Principle of Superposition.

**Field
Lines**

Field lines are used to indicate the direction of force in all directions from a source. Some basic rules:

- Electric field lines start on positive charges and end on negative charges. The arrows on the field lines should be drawn that way.
- Lines are drawn so they are perpendicular to the point.
- Strong fields show more lines spaced closer together than weak fields.
- Lines get closer together as they get closer to the source.
- Field lines never intersect!

To see some good pictures and read more on the subject, check out some of the following. There is a lot of good stuff here!

http://www.physicsclassroom.com/Class/estatics/u8l4c.html

http://www.colorado.edu/physics/2000/applets/nforcefield.html

http://www.gel.ulaval.ca/~mbusque/elec/main_e.html

http://hyperphysics.phy-astr.gsu.edu/hbase/electric/elefie.html

http://www.colorado.edu/physics/2000/waves_particles/wavpart3.html

http://www.physicsclassroom.com/Class/estatics/u8l4d.html

The NTNU provides some great applets for Physics. Click here for an applet that demonstrates charges moving in Electric Fields.

Also, here is another applet you can check out for Electric Fields: http://www.cco.caltech.edu/~phys1/java/phys1/EField/EField.html

For Practice Problems, Try:

*Giancoli Multiple Choice Practice Questions (Go ahead - try a
few.)*