We may define electrostatic potential at a point in an electrostatic field as the amount of work done in moving a unit positive test charge from infinity to that point against the electrostatic forces, along any path. Due to a single charge \( q \), potential at a point distant \( r \) from the charge is \( V=\frac{q}{4 \pi \epsilon_{0} r} \). The potential can be positive or negative. However, it is a scalar quantity. The total amount of work done in bringing various charges to their respective positions from infinitely large mutual separations gives us the electric potential energy of the system of charges. Whereas electric potential is measured in volt, electric potential energy is measured in joule. You are given a square of each side 1.0 metre with four charges \( +1 \times 10^{-8} \mathrm{C},-2 \times 10^{-8} \mathrm{C},+3 \times 10^{-8} \mathrm{C} \) and \( +2 \times 10^{-8} \mathrm{C} \) placed at the four corners of the square. With the help of the passage given above, choose the most appropriate alternative for each of the following questions :
Potential energy of the system of four charges is
(a) \( 12.73 \times 10^{7} \mathrm{~J} \)
(b) \( -6.4 \times 10^{-7} \mathrm{~J} \)
(c) \( 12.73 \times 10^{-9} \mathrm{~J} \)
(d) \( -12.73 \times 10^{-9} \mathrm{~J} \)
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