Learning goal: to practice problem-solving strategy 20.1 electric forces and coulomb's law. two charged particles, with charges q1=q and q2=4q, are located at a distance d=2cm apart on the x axis. a third charged particle, with charge q3=q, is placed on the x axis such that the magnitude of the force that charge 1 exerts on charge 3 is equal to the force that charge 2 exerts on charge 3. find the position of charge 3 when q = 1.0 nc . note that you are given the magnitude of q, but the sign of the charge q is not specified. q can be positive or negative, so that the three charges (q1, q2, q3) are either all positive charges or all negative charges.

1) Let's put  and  both on the x-axis such that  is on the right side of . The distance between the two charges is . 

2) Let's put  on the x-axis and let's call  the distance between charge 1 and charge 3. As a consequence, the distance between charge 2 and 3 will be : if r is positive, then charge 3 will be located on the left of charge 1, if r is negative, charge 3 will be located between charge 1 and charge 2.

3) The electrostatic force between charge 1 and charge 3 is

while the force between charge 2 and charge 3 is


4) The problem says the two forces are equal in intensity. Therefore we can write . Using the equations written at step 3), and substituting and  as mentioned in the problem,  becomes

Using , we can solve the equation, and we get two solutions:


Both solutions are correct. With the former, the charge 3 is located 2 cm on the left of charge 1, while with the latter, charge 3 is located 0.67 cm on the right of charge 1, between charge 1 and 2.