For a Positive Charge the field comes out of the charge and falls off a 1/r^2 which means if i double my distance away for the charge the strength of the field is a 1/4 of it's original strength, triple the distance and the strength is 1/9 it's original strength

 For a Negative Charge the field goes into the charge and falls off a 1/r^2 which means if i double my distance away for the charge the strength of the field is a 1/4 of it's original strength, triple the distance and the strength is 1/9 it's original strength

 The presence of an electric charge produces a force on all other charges present. The electric force produces 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. At a certain moment charge q2 is moved closer to charge q1. As a result we expect an increase of the force exerted by q2 on q1. However, this change can not occur instantaneous (no signal can propagate faster than the speed of light). 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 it 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:

The electric field can be represented graphically by field lines. These lines are drawn in such a way that, at a given point, the tangent of the line has the direction of the electric field at that point. The density of lines is proportional to the magnitude of the electric field. Each field line starts on a positive point charge and ends on a negative point charge. Since the density of field lines is proportional to the strength of the electric field, the number of lines emerging from a positive charge must also be proportional to the charge. An example of field lines generated by a charge distributions is shown in Figure 23.9.

 

Point Charge:

 A point charge is a hypothetical charge located at a single point in space. Point charges like point masses are use to solve for field strength at a given point.

Insulators and Conductors: 

Every piece of matter is composed of electrons and protons, meaning that every piece of matter carries a charge.  Most of the time these charges are balanced leaving a next charge of zero. When matter is exposed to an electric field these charges are either attracted or repelled by the field (depending on the charge and the field).  In some cases some of  the electrons will be liberated from one atom and move to the next.  This motion of electrons is what is refereed to as current.

        Insulators are pieces of matter that don't give up their electrons easily, making then inert in an electric field, and unable to carry a current. 

        Conductors are pieces of matter that give up their electrons freely, making them very reactive to electric fields.  Conductors are used as a wires in electrical circuits because of how well they can carry a current.

Insulators and Electric Field

A sphere made of an insulative material is exposed to an electric field.

As the electric field interacts with the sphere, if the Net charge of the sphere is zero, then the interaction with the sphere is zero.  The sphere is inert.  The external field doesn't change inside and outside of the sphere.  The external field acts as if there is no sphere.

If the insulator is charged, the external field behaves as if a charged particle replaced the sphere at the center of the sphere up until radius of the sphere.  Inside the sphere the electric field increases or decreases linearly depending on charge of the sphere until it reaches the center of the sphere.

At the spheres center the insulator doesn't contribute to the net electric field, so the field at that point is the external field. 

Moving beyond the center of the sphere, electric field decreases or increases (its the opposite direction as when you move from the edge of the sphere to the center).

Conductors and Electric Fields: 

A sphere made out of a conductive material is exposed to an electric field.

If the sphere is a conductor, which allows charges to move freely about the surface, electrons move towards the electric field, but the protons are fixed in place.  The exiting electrons leave behind what's called a hole (that really what it's call) of positive charge. 

Negative and positive charges are now on opposite ends of the sphere.
With the electrons and protons on opposite sides of the conductive sphere, the sphere then becomes polarized.  The charges on the sphere create there own electric field.  The electric field is refereed to as a "Induced Electric Field" because it was created by an external electric field.

The external field keeps separating the charges until the internal electric field grows strong enough to counter act the external field, when the strength of both fields are equal.

External Electric Field = - Internal Electric Field

The net electric field inside the sphere goes to zero, but the external electric field remains unchanged, it behaves as if the conducting sphere is not even there.