Answer:
The value of q is

Step-by-step explanation:
Given that,
Each charge = -Q
Distance between charges = L
Reduced force =

Suppose, Two particles each with a charge -Q are fixed a distance L apart as shown above. Each particle experiences a net electric force F. A particle with a charge +q is now fixed midway between the original two particles.
We know that,
The force on each end is
...(I)
If the charge q is placed at mid point then
The force on each end charge is
....(II)
We need to calculate the value of q
Using equation (II)

Put the value of F into the formula




Hence, The value of q is
