A conducting sphere is charged. If the electric field at a distance 20 cm from the centre of the sphere is \( 1.2\times10^{3}\,\mathrm{NC^{-1}} \) and points radially inwards, the net charge on the sphere is :
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → \( -5.3\times10^{-9}\,\mathrm{C} \)
By Gauss's law, outside a charged sphere the field is the same as if the whole charge were at the centre:
\( \displaystyle E = \frac{1}{4\pi\varepsilon_0}\,\frac{|q|}{r^{2}} \;\Rightarrow\; |q| = 4\pi\varepsilon_0\,E\,r^{2} \)
\( r = 20\,\mathrm{cm} = 0.2\,\mathrm{m} \)
\( 1/4\pi\varepsilon_0 = 9\times10^{9}\,\mathrm{N\,m^{2}\,C^{-2}} \)
\( \displaystyle |q| = \frac{1.2\times10^{3} \times (0.2)^{2}}{9\times10^{9}} = \frac{48}{9\times10^{9}} = 5.3\times10^{-9}\,\mathrm{C} \)
The field points radially inwards, towards the sphere, so the charge is negative:
\( \displaystyle q = -5.3\times10^{-9}\,\mathrm{C} \)
Note: NTA picked this question from an NCERT (2026-27) exercise and changed the figures. Do not ignore NCERT while practising numericals.
NCERT (2026-27):
Exercises – …
