Read the following passage and answer the questions.
A student studies the charges on four very tiny plastic beads, P, Q, R and S. All four beads are neutral at the start. She charges each bead by rubbing it with a different material. A sensitive meter then gives the charge on each bead. Her readings are: P, \(+8.0\times10^{-19}\ \mathrm{C}\); Q, \(-4.8\times10^{-19}\ \mathrm{C}\); R, \(+3.2\times10^{-19}\ \mathrm{C}\); and S, \(-1.6\times10^{-19}\ \mathrm{C}\).
Next, she puts all four beads in a small closed box. The beads can touch one another inside the box, but no charge can enter or leave it. She also compares each reading with the magnitude of the charge on an electron, \(1.6\times10^{-19}\ \mathrm{C}\). Her teacher tells her that charged bodies in everyday experiments carry much larger charges, of a few microcoulombs.
After the beads have touched one another inside the box, what is the total charge of the four beads?
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → \(+4.8\times10^{-19}\ \mathrm{C}\)
Touching can move charge from one bead to another. The box lets no charge in or out, so the total charge does not change. The total is the algebraic sum of the four charges, taken with their signs.
\( \begin{aligned} q_{\text{total}} &= q_P+q_Q+q_R+q_S \\ &= (+8.0-4.8+3.2-1.6)\times10^{-19} \\ &= +4.8\times10^{-19}\ \mathrm{C} \end{aligned} \)
From the above, the total charge is \( +4.8\times10^{-19}\ \mathrm{C} \) before and after the beads touch.
NCERT (2026-27):
Additivity of charges – “If a system contains n charges q1, q2, q3, …, qn, then the total charge of the system is q1 + q2 + q3 + … + qn .”
Charge is conserved – “Within an isolated system consisting of many charged bodies, due to interactions among the bodies, charges may get redistributed but it is found that the total charge of the isolated system is always conserved.”