A charge of \( 8.0 \times 10^{-9}\,\mathrm{C} \) is uniformly distributed on the surface of a spherical shell of radius 10 cm. The electric field at a distance of 10 cm from the outer surface of the shell is
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → \( 1.8 \times 10^{3}\,\mathrm{N/C} \)
By Gauss's law, outside a uniformly charged spherical shell the field is the same as if the whole charge were placed at the centre. The distance must therefore be measured from the centre, not from the surface.
\( \displaystyle r = 10\,\mathrm{cm} + 10\,\mathrm{cm} = 20\,\mathrm{cm} = 0.20\,\mathrm{m} \)
\( \displaystyle E = \frac{1}{4\pi\varepsilon_0}\,\frac{q}{r^{2}} = \frac{9\times10^{9} \times 8.0\times10^{-9}}{(0.20)^{2}}\,\mathrm{N/C} \)
\( \displaystyle E = \frac{72}{0.04}\,\mathrm{N/C} = 1.8\times10^{3}\,\mathrm{N/C} \)