Problem 2

A point charge is at the point , , and a second point charge is at the point , .  Find the magnitude and direction of the net electric field at the origin.

Solution

The magnitude of electric field due to charge 1 is

The magnitude of electric field due to charge 2 is

To find the net electric field we need to find the vector sum of electric field due to charge 1 and electric field due to charge 2. It is easier to work in term of components. So the x-component of the net electric field is the sum of x-components of electric field due to charge 1 and due to charge 2, and the y-component of the net electric field is the sum of y-components of electric field due to charge 1 and due to charge 2.

The x and y components of electric field due to charge 1 are

Both components are positive since the charge is negative.

The x and y components of electric field due to charge 2 are

It is negative since the charge is positive.

Then we can find the x and y components of the net electric field:

Then we can find the magnitude of the net electric field:

The direction of electric field is determined by the angle between the vector of electric field and axis x: