Question

charge Q is shared by two bodies . What are the individual charges such that each exert maximum force of interaction on other?

Answer 1

Answer:

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.

Explanation:

Step 1: Calculation of force

Let one part of the charge be q. Thus other part of the charge is Q−q

From Coulomb's law:

Electrostatic force between them F=

r

2

kq(Q−q)

Step 2: Condition of maximum force

For maximum force,

dq

dF

=0

∴

dq

d

(

r

2

kq(Q−q)

)=0

Or,

dq

d

(qQ−q

2

)=0

Or, Q−2q=0

⇒ q=

2

Q

Hence force between them is maximum if the two parts have equal charge Q/2 each