Question

A charge Q is to be divided into two parts so that the force between the parts will be maximum. The
parts are 1)Q/2,Q/2 2)Q/4,Q/4 3)Q/3,Q/3 4)Q/6,5Q/6​

Answer 1

Given :

A charge Q is divided in such a way that the force between the parts will be maximum.

To Find :

Charge on both parts.

Solution :

❒ The magnitude of electrostatic force between two point charges is directly proportional to the product of charges and inversely proportional to the square of the first between them.

• This is known as Coulomb's law also known as inverse square law.

$\sf:\implies\:F=\dfrac{kq_1q_2}{r^2}$

Let charge on first part be q and on second part be Q - q

For maximum value of F, dF/dq should be zero.

$\sf:\implies\:\dfrac{dF}{dq}=0$

$\sf:\implies\:\dfrac{d}{dq}\bigg[\dfrac{kq(Q-q)}{r^2}\bigg]=0$

$\sf:\implies\:\dfrac{d}{dq}(qQ-q^2)=0$

$\sf:\implies\:Q-2q=0$

$\sf:\implies\:2q=Q$

$:\implies\:\underline{\boxed{\bf{\gray{q=\dfrac{Q}{2}}}}}$

Charge on second part :-

➙ q₂ = Q - q

➙ q₂ = Q - Q/2

➙ q₂ = Q/2

∴ (1) is the correct answer!