For q3 to be in equilibrium the total force acting on it has to be zero.
Let's say that total distance traveled by car is L (this is just for the convenience).
We can set up a system of equations to find an answer. Let's say that from q1 to q3 the distance is r_1 and from q3 to q2 the distance is r_2, we know that this distance has to be equal to:
The second equation is going to the total force acting on the charge q3:
k_c is the Coulomb's constant. Since left-hand side is zero we just divide whole equation with k_c to get rid of it:
Let's solve this for r_1^2:
Now we have a quadratic equation with following parameter:
We know that two solutions are:
We need a positive solution. When we plug in all the numbers we get:
Let's say that total distance traveled by car is L (this is just for the convenience).
We can set up a system of equations to find an answer. Let's say that from q1 to q3 the distance is r_1 and from q3 to q2 the distance is r_2, we know that this distance has to be equal to:
The second equation is going to the total force acting on the charge q3:
k_c is the Coulomb's constant. Since left-hand side is zero we just divide whole equation with k_c to get rid of it:
Let's solve this for r_1^2:
Now we have a quadratic equation with following parameter:
We know that two solutions are:
We need a positive solution. When we plug in all the numbers we get: