A charge 2Q is located at the origin while a second charge –Q is located at x = a. Where should a third charge be placed so that the net force on the charge is zero?

If the third charge is placed at a distance the net force on the charge will be zero

Explanation:

Consider the diagram below.

Let us add a new charge Q at a distance b from the origin.

Let the force that the charge 2Q exert on the new charge (Q) be

Let the force that charge -Q exerts on the new charge be

For the third charge in equilibrium,

Solving this will give us a quadratic equation which will be further simplified.

Making b the subject of the formula, we can get the distance that the third charge will be placed .

So if the third charge is placed at a distance the net force on the charge will be zero

if real values were plugged in, it will be easier for us to determine the value of b

its c i just checked it