The electirc field intensity at a distance of 20 cm from the centre of a small conducting sphere is \( 1.5 \times 10^{3}\,\mathrm{N\,C^{-1}} \) and is directed towards the sphere. The charge on the sphere is
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → - 6.6 nC
The electric field of a point-like charged sphere points away from a positive charge and towards a negative charge. The field here is directed towards the sphere, so the charge is negative. Its magnitude follows from
\( \displaystyle E = \frac{k\,|q|}{r^{2}} \;\Rightarrow\; |q| = \frac{E\,r^{2}}{k} \)
\( r = 20\,\mathrm{cm} = 0.2\,\mathrm{m} \)
\( \displaystyle |q| = \frac{1.5\times10^{3}\times(0.2)^{2}}{9\times10^{9}} = \frac{60}{9\times10^{9}} = 6.7\times10^{-9}\,\mathrm{C} \approx 6.6\,\mathrm{nC} \)
So \( q = -6.6\,\mathrm{nC} \) (the value \( 6.67\,\mathrm{nC} \) is given in the option as 6.6).