Question

4 A small object has charge Q. Charge q is removed from it and placed on a second small object. The two objects are placed 1 m apart. For the force that each object exerts on the other to be a maximum, q should be:
2Q
Q
Q/2
Q/4

Answer 1

According to Couloumb's law:
F=k*q1*q2/r^2
F=k*q*(Q-q)/r^2
k=const
and r=1 m
F is proportional to q*(Q-q)=q*Q-q^2
The zero point of the derivative of F'=0 gives the maximum point.
THe derivative F' is proportional to Q-2q, therefore
Q-2q=0
q=Q/2