Question

6 A charge Q is to be divided on two objects. What should be the values of the charges on the objects so that the force between the objects can be maximum? Soln: Suppose one object receives a charge q and the other Q-e. The force between the objects is​

Answer 1

Suppose one object receives a charge q and the

other Q-q. The force between the objects is

F=q(Q−q)4πε0d2,

where d is the separation between them. For F to be

maximmum, the quantity

y=q(Q−q)=Qq−q2

Should be maximum. This is the case when,

dydq=0or,Q−2q=0or,q=Q2

Thus, the charge shuld be divided equally on the two objects.

$\huge \pink{~} \red {τ} \green {α} \blue {v} \orange {v} \pink {u} \red {♡}$

Answer 2

Suppose one object receives a charge q and the

other Q-q. The force between the objects is

F=q(Q−q)4πε0d2,

where d is the separation between them. For F to be

maximmum, the quantity

y=q(Q−q)=Qq−q2

Should be maximum. This is the case when,

dydq=0or,Q−2q=0or,q=Q2

Thus, the charge shuld be divided equally on the two objects.