A field provides the force to move a specific body. It does this by creating an invisible "structure" in space that interacts with a specific type of particle or a specific property of a particle.

Simple fields have two characteristics, a variable that determines the field's strength and a variable describing a property that the field needs to exert any kind of force. ("Simple" means the math used to model the fields are linear.) When physicists look closer at the causes of the fields, the math models may not be so simple. Take gravity for example.

The pull of gravity on a body on the Earth is called, weight. It is described as

w = mg

Where "w" is the force of gravity in Newtons, "m" is the mass, and "g" is the acceleration due to gravity near the Earth's surface. "g" is also called the field strength variable. The field strength variable defines the strength of the field, regardless of the nature of the body that is in the field. In this case the field strength describes the acceleration due to the pull of gravity. The "m" in the formula is the property that gravity affects and multiplies the field strength to show the over all force.

Object

Field Strength

Earth

9.80 ^{m}/_{s}2

Moon

1.67 ^{m}/_{s}2

Sun

274 ^{m}/_{s}2

"m," mass, is the variable that gravity affects. If a body has mass then gravity affects it. The amount a body is affected is found by multiplying mass times field strength variable. But, if you examine gravity closer and create a math model to describe gravity under all circumstances then the formula is not linear any more. It is

Electric fields, on a macro scale, are also simple. The force of anything with a charge can be described with the math model of

F = qE

F

force felt on anything with a charge

Newtons [ N ]

q

charge on a body

Coulombs [ C ]

E

Electric Field Strength

When we look closer at the cause of the force we will see it is also not so simple. It follows something called Coulomb's Law.

(Coulomb's Law will be covered later in more detail.) The electric field is a vector. Which means it has magnitude and direction. The magnitude is determined by the equation F=qE. the direction and strength is represented with a vector field.

Note:

Many physicists will substitute "k" for constant. (You will not see "k" used on the AP equation sheets, but it is handy and used a lot.)

A handy trick to save you time is to save 8.99x10^{9} into the variable "k" in your graphing calculator. Whenever you need to use the constant in your calculations, type the letter "k" on your calculator.

Click here if you want to see a short YouTube video on how to store a number on a TI graphing calcualtor. [ Link goes here. ]

Vector e-field

The first way to determine the electric field's direction is by something called a vector field. The vector field is a collection of vectors that show the electric field's direction and magnitude and various locations in space. Below is what the vector field for a positively charged body would look like.

The tail of the vectors represent the location of the electric field's measurement. The length of the vector represents the electric field's strength at that location. The electric field's direction is shown by the vector's direction.

Simple Motion in a Field

To accelerate a particle an unbalanced force needs to be applied. This force can come from contact or from a force field. The force field can push the particle without "touching" it. One such force field is gravity. Gravity pulls everything with mass. The Moon is held in orbit because it is caught in the Earth's gravitational field. Some asteroids that pass near the Earth have their path altered when they get in the Earth's gravitational field.

The animation above shows that an object with mass, will travel along the gravitational field line when placed at rest. A g-field line is the path an object with mass will travel. An electric field can do the same thing to everything with a charge.

Again, this shows that a charged object will travel along the field lines. However, unlike gravitational field lines, positively charged particles follow the lines in the arrow's direction and negative charges travel in the opposite direction the arrows direction. This is because an electric field is defined as the path a positive particle would travel.

by Tony Wayne ...(If you are a teacher, please feel free to use these resources in your teaching.)