Electric field equation

The electric field equation is shown below. Before we get to it, ask yourself this question, " What is an electric field? "

Suppose an object is charged with a positive charge q0 and then you place a second positive charge q1 near the object. We are going to call q1 a 'test charge'
Charged object
According to Coulomb's law, we know that q0 will exert a repulsive electrostatic force on q1.

If we get enough data, we know that we can measure this force in no time.

However, notice that the test charge did not actually touch the charged object. 

Therefore, many people may ask themselves this question, " How does the charged object know that the test charge is in the neighborhood? "

We answer this question by saying that there is a force field, more specifically, an electric field in the space surrounding the charged object.

Electric field
In our illustration immediately above, you see only 1 vector in green that represents the electric field around the charged object at q1.

The electric field is however a vector field with more than one vector.

Use one vector for each charge around the charged object and an electric field will look like the graph you see below.

Electric field

The electric field equation measures the force exerted on just 1 small test charge placed in the field.

Say you want to measure the electric field due to a test charge q1.

The electrostatic force per charge is E =
F / q1

Important observation about the first illustration above.

Since q0 is far from q1, this is " action at a distance "

Action at a distance can be mind-boggling and this has even troubled Isaac Newton and many others physicists. 

Nonetheless, when we think about it deep enough, we will see that action at a distance can happen with iron filings and a magnet.

It is also happening with objects placed near the earth in space. These objects will be in a gravitational field as they each experience the force of gravity. 

The gravitational field around the earth is what keep a satellite in its orbit near the earth.

Another way to express the electric field equation

Say a charge q1 is placed at a distance d from a charged object.

To find the electrostatic force due to a charged object q, we can use the formula.


F = k
|q||q1| / d2

We can find another equation for the electric field by combining the following 2 equations.

E =
F / q1
F = k
|q||q1| / d2

E = k
|q||q1| /d2 / q1

Notice that since q1 is positive as already stated earlier, |q1| = q

E = k
|q|q1 /d2 / q1
E = k
|q|q1 /d2 / q1

q1 is cancelled since it is on top and at the bottom.

E = k |q| / d2

E = k
|q| / d2

Electric field equation quiz

An electric field quiz to test your understanding of electric field. You will not need to use a paper and pencil to complete this quiz.

First, read this lesson about electric field and then take this quiz.

Objective of the quiz:

  • Know what a test charge is.
  • Know what an electric field is.
  • Know what action at distance is
  • Know which formula to use for the electric field
  • Know the difference between test charge and charged object.
  • Understand how an electric field is created
Test your knowledge with the quiz below:

Electric field lines