Two charges 5 μC and -2 μC (with no external field) are placed at (-9 cm, 0, 0) and (9 cm, 0, 0) respectively. The work required to separate the two charges infinitely away from each other is:

0.5 J

The correct answer is Option (2) → 0.5 J

The key to this problem is understanding that the "work required to separate the two charges infinitely away from each other" is the negative of the initial potential energy of the system(W = - U initial). This is because the final potential energy at infinite separation is zero (U final = 0).

So, work done by an external agent is W= U final - U initial

                                                                   = 0- U initial

                                                                    = -U initial

The initial potential energy of the system (${U\_}^{initial}$): $U=\frac{Lq_1q_2}{r}$

where,

$q_1=5μc=5×10^{-6}C,q_2=-2μc=-2×10^{-6}C$

$r$, Distance between two charges = $9cm-(-9cm)$

$=18cm$

$=0.18m$

$∴U=\frac{(9×10^9)(5×10^{-6})(-2×10^{-6})}{0.18}$

$=-0.5J$

Since this is the potential energy of the system, the work required to separate the charges to infinity is the negative of this value:

Thus,

W= - (U initial)

W= - (- 0.5 J) = 0.5