A metal cube of side 0.1 m is uniformly charged by \( 18\,\mu\mathrm{C} \). Its surface charge density will be
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → \( 3 \times 10^{-4}\,\mathrm{C\,m^{-2}} \)
The surface charge density is the charge per unit area of the surface, \( \sigma = q/A \). The charge on a metal cube spreads over its whole surface, which has six faces.
\( \displaystyle A = 6a^{2} = 6 \times (0.1\,\mathrm{m})^{2} = 0.06\,\mathrm{m^{2}} \)
\( \displaystyle \sigma = \frac{q}{A} = \frac{18\times10^{-6}\,\mathrm{C}}{0.06\,\mathrm{m^{2}}} = 3\times10^{-4}\,\mathrm{C\,m^{-2}} \)