A neutral metal sphere is given a charge of \( -1.6\,\mu\mathrm{C} \). By how much does its mass increase? (Take \( e=1.6\times10^{-19}\,\mathrm{C} \) and mass of an electron \( =9.1\times10^{-31}\,\mathrm{kg} \))
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → \( 9.1\times10^{-18}\,\mathrm{kg} \)
A neutral body becomes negatively charged by gaining electrons, and each electron brings its own mass with it. The number of electrons added follows from the quantisation of charge, \( q=ne \). The gain in mass is that number times the mass of one electron.
The number of electrons added to the sphere is:
\( \begin{aligned} n &= \frac{|q|}{e} \\ &= \frac{1.6\times10^{-6}\,\mathrm{C}}{1.6\times10^{-19}\,\mathrm{C}} \\ &= 10^{13} \end{aligned} \)
The increase in mass is:
\( \begin{aligned} \Delta m &= n\,m_e \\ &= 10^{13}\times9.1\times10^{-31}\,\mathrm{kg} \\ &= 9.1\times10^{-18}\,\mathrm{kg} \end{aligned} \)
NCERT (2026-27):
Electric Charge – “… In solids, some of the electrons, being less tightly bound in the atom, are the charges which are transferred from one body to the other. A body can thus be charged positively by losing some of its electrons. Similarly, a body can be charged negatively by gaining electrons.”