Any number of particles with a net charge will feel either an attraction or repulsion from the other charges. This force is an electric force. This force is modeled by Coulomb's Law.
Math Background
in order to conserve space, scientist and engineers use a math short hand to represent certain powers of ten. The table below show the short hand and how it is used. (Learn these prefixes.)
The display on a calculator can only display a specific number of digits across the screen before it runs out of room. Calculator manufactures wanted to create symbol the would use up less screen space when displaying exponents raised to a power of ten. They created a shorthand so calculators could "text" you the answer while being able to fit more meaningful numbers on the screen. The shorthand looks like this
6E-3
The "E" take the place of "x10" Do not write down "E-3" or "E" anything when showing your work. The "E" is text messaging shorthand. It is not an excepted math practice. Instead you should write the number as
6x10-3.
The basics
Figuring out the force between two charged particle is a two step process.
Figure out if the particles are attracted or repelled.
Calculate the magnitude of the force between the particles using Coulomb's Law.
Figuring Out Direction
Two charges are separated by the distance shown. What is the force felt on the negative charge?
To figure out the direction os the electric force on a charge, use the main rule for the charge model,
"Opposites attract, likes repel."
Since these two charges have opposite signs, their forces will attract each other.
The negative charge will feel a force pulling it to the left. The positive charge will feel and equal and opposite force pulling it to the right. Since the original question was about the negative charge, ignore what happens to positive, blue, charge. The magnitude of this force is calculated from Coulomb's Law.
Coulomb's Law & Calculating the Forces's Magnitude
Charles A. de Coulomb came up with a math model for describing the magnitude of the force of attraction between any two charges. The equation he came up with is referred to as Coulomb's Law and is shown below.
Note that the q's are the charges' magnitudes. Do not put the negative signs in the equation. At this point plug in the numbers.
A couple of things to note about the solution. The negative signs on the charges were dropped. This is because the equation is being used to calculate the magnitude of the force and not the direction. The direction was calculated in the first by using the charge model's rule. Also note the givens are listed when solving the problem.
Free Body Diagrams as an Equation
To be successful at solving problems with multiple charges, freebody diagrams must be mastered. The freebody diagram will create the equation that is used to calculate the answer.
Example #2 Multiple Charges in a Line
Find the net force on charge "B."
Quick overview of the solution steps.
Identify the directions of the forces acting on the particle in question using the charge model's rule that opposites attract and likes repel.
Create a free body diagram from these forces.
IF the charges do not ALL line up in a straight line, find the vertical and horizontal components of each force and combine the components by summing up the forces in the "X" and then the "Y" directions.
Find the magnitude of each force. This means to ignore the plus and minus signs on the charges when doing the math.
Plug in the magnitudes into the equation created from the free body.
Solve.
Click the embedded video to see the solution.
Interactive practice
On more problem of three charges in a plane.
by Tony Wayne ...(If you are a teacher, please feel free to use these resources in your teaching.)
