Three charges lie along the x axis. the positive charge q1 = 15 μc is at x= 2.0 m and the positive charge q2 = 6.0μc is at the origin. where must the negative charge q3 be placed on the x axis so that the resultant electric force on it is zero?

The charge q3 must lie in .

Explanation:

For the net force to be zero in q3, the positive charges must be pulling with the same force but in opposite directions. So

,

where is the force exerted by q1 on q3 and   is the force exerted by q2 on q3.

Recalling the Coulomb's law, we know that the magnitud of the electric force between two charges and is:

,

where is Coulomb's constant and is the distance between the charges.

In addition to this, it is also important to remember that like charges repel each other and unlike charges attract.

So, we have:

,

,

,

and remembering that

,

,

wich leads us to

,

and this is a quadratic equation.

The solutions to this equation are:

This two are solutions of the equation, even so, only one is a correct solution to the problem. The correct answer is

.

This is because q3 must lie between q1 and q2 so the attractive forces cancel each other.