If a system consists of two charges 4 µC and -3 µC with no external . . .

Question :  If a system consists of two charges 4 µC and -3 µC with no external field placed at (-5 cm, 0, 0) and (5 cm, 0, 0) respectively. The amount of work required to separate the two charges infinitely away from each other is

(a) 1.1 J
(b) 2 J
(c) 2.5 J
(d) 3 J

Doubt by Zoya

Solution : 

q1=4×10-6 C
q2=-3×10-6 C
r  =5-(-5) = 10 cm = 10×10-2 m
r  = 10-1 m

Initial potential energy stored in the system
U1 = kq1q2/r
U1 = 9×109×4×10-6×(-3×10-6)/10-1
U1 = -108/100
U1 = -1.08 J

Final potential energy stored in the system when they are separated infinitely away from each other
U2 = 0 J

Amount of work required 
= change in PE of system 
= U2-U1
= 0-(-1.08)
= +1.08 J
= 1.1 J (approx)

Hence, a) 1.1 J would be the correct option.