Two identical small metal spheres A and B carry charges of \( +6\,\mu\mathrm{C} \) and \( -2\,\mu\mathrm{C} \) respectively. They are touched together and then separated. During the contact (Take \( e=1.6\times10^{-19}\,\mathrm{C} \))
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → \( 2.5\times10^{13} \) electrons move from B to A
When the two spheres touch, the total charge of the pair is conserved. As the spheres are identical, this charge is shared equally. Only electrons move in a metal, and the number transferred follows from the quantisation of charge, \( q=ne \).
The charge on each sphere after contact is:
\( \begin{aligned} q &= \frac{(+6\,\mu\mathrm{C})+(-2\,\mu\mathrm{C})}{2} \\ &= +2\,\mu\mathrm{C} \end{aligned} \)
Sphere A goes from \( +6\,\mu\mathrm{C} \) to \( +2\,\mu\mathrm{C} \), so it gains \( 4\,\mu\mathrm{C} \) of negative charge. Sphere B goes from \( -2\,\mu\mathrm{C} \) to \( +2\,\mu\mathrm{C} \) and loses the same amount. The number of electrons that pass from B to A is:
\( \begin{aligned} n &= \frac{\Delta q}{e} \\ &= \frac{4\times10^{-6}\,\mathrm{C}}{1.6\times10^{-19}\,\mathrm{C}} \\ &= 2.5\times10^{13} \end{aligned} \)
Hence, \( 2.5\times10^{13} \) electrons move from B to A.
NCERT (2026-27):
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.”
Summary – “… Quantisation of electric charge means that total charge (q) of a body is always an integral multiple of a basic quantum of charge (e) i.e., q = n e, where n = 0, ±1, ±2, ±3, .... Proton and electron have charges +e, –e, respectively.”