Three point charges are placed at the corners of an equilateral triangle ABC as shown. The work done to put together these charges from infinity to their respective locations is
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → \( -3.42 \times 10^{-4}\,\mathrm{J} \)
The work done in assembling the charges equals the electrostatic potential energy of the system, which is the sum of the energies of every pair of charges.
\( \displaystyle W = U = \frac{1}{4\pi\varepsilon_0\,r}\left(q_1 q_2 + q_2 q_3 + q_3 q_1\right) \)
Reading the figure:
\( q_1 = +3\times10^{-8}\,\mathrm{C}, \quad q_2 = -5\times10^{-8}\,\mathrm{C}, \quad q_3 = +2\times10^{-8}\,\mathrm{C} \)
\( r = 5\,\mathrm{cm} = 0.05\,\mathrm{m} \text{ for every pair} \)
The sum of the pair products, with signs:
\( q_1 q_2 + q_2 q_3 + q_3 q_1 = (-15 - 10 + 6)\times10^{-16} = -19\times10^{-16}\,\mathrm{C^2} \)
\( \displaystyle U = \frac{9\times10^{9}}{0.05} \times (-19\times10^{-16}) = 1.8\times10^{11} \times (-19\times10^{-16}) \)
\( \displaystyle U = -3.42\times10^{-4}\,\mathrm{J} \)
The negative sign means the attraction of the negative charge to the two positive charges outweighs the repulsion between the positive pair, so the external agent does negative work.