Question

1. A charge Q is divided into two parts q and Q-q and separated by a distance
R. The force of repulsion between them will be maximum when:
a. q = Q/4
b. q = Q/2
c. q= Q
d. None of these​

Answer 1

(c) if q=Q, force F=0

Hence the force of repulsion between them will be maximum when q= Q/2

Answer 2

Given:-

• A charge is divided into two parts

To find:-

• Max force of repulsion will be at

Solution:-

As the charge is divide in two parts q and Q-q than the force acting between both charges will be:-

$\large\rightarrow F=\frac{Kq_1 q_2}{R^2}$

$\large\rightarrow F=\frac{Kq(Q-q)}{R^2}$

$\large\rightarrow F=\frac{K(Qq-q^2)}{R^2}$

Now to find maximum force we will use concept of maxima

$\large\rightarrow \frac{df}{dq} = \frac{K(Q-2q)}{R^2} =0$

$\large\rightarrow Q-2q=0$

$\large\rightarrow \frac{Q}{2}=q$

$\large\red{\boxed{Answer :\:q=\frac{Q}{2}}}$