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'
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.

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.

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 

An electric field will look like the graph you see below.

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.

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 thing 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 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.

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

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

E = k |q| / d²