Question

two charges q and 4q are a distance apart a third charge Q is placed at a middle of line joining then what should be magnitude and nature so that net force is zero

Answer 1

This is the position where the third charge should be placed. Now, we have to determine the nature and magnitude of it. For this just try to satisfy the condition of equilibrium on any one of the remaining two charges. Let's take +q charges. The force on it due to +4q charge is directed left wards so force on it due to the third charge should be directed right wards. This implies that the force between +q charge and third charge should be of attractive nature. Thus the nature of the 3rd charge is (−ve).

Taking the third charge to be −Q (say) and then on applying the condition of equilibrium on +q charge