Electric Field: A Numerical Example

We have looked at Coulomb's Law, the definition of the electric field, and applied that to find the electric field due to a point charge. Now we turn to an example with more than a single point charge.

With three point charges q₁, q₂, and q₃ located as shown in the diagram below, what is the electric field E at point P?

With three point charges q₁, q₂, and q₃ located as shown in the diagram above, what is the electric field E at point P? There is not necessarily any charge at point P. An electric field E at point P (or any other point) means that _if_ a "test charge" q is brought to that point, that "test charge" q will find a force F that is given by F = E q.

We know how to find the electric field caused by a single point charge. We will find the electric field E₁ caused by charge q₁, the electric field E₂ caused by charge q₂, and the electric field E₃ caused by charge q₃. The net electric field E_net is the _vector_ sum of these three fields,

E_net = E₁ + E₂ + E₃

Remember, tho', this is true only as a vector equation!

Start with E₁, the electric field caused by charge q₁,

E₁ = 1.79 x 10 ^{5 N}/_C

Remember, this is a vector addition problem so we will need the vector components of all the electric fields.

Now we turn our attention to E_2, the electric field caused by charge q₂,

Now we turn our attention to E_3, the electric field caused by charge q₃,

Now we've done all the hard work.

All that remains it to put the pieces together. It is just another vector addition problem.

Don't forget, however, that it _is_ a vector problem!

 

 

 

We're almost done!

Now we need to find the magnitude of the electric field and its direction.

Electric Field Due to a Point Charge			Electric Fields from Line and Plane Charges
Return to Ch 17, Electrostatics & Electric Energy

(c) Doug Davis, 2002; all rights reserved