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A conducting sphere of radius $10\, cm$ has unknown charge. If the electric field at a distance $20\, cm$ from the centre of the sphere is $1.2 \times 10^3\, N\, C^{-1}$ and points radially inwards. The net charge on the sphere is
$ - 4.5 \times {10^{ - 9}}\,C$
$ 4.5 \times {10^{9}}\,C$
$ - 5.3 \times {10^{ - 9}}\,C$
$ - 5.3 \times {10^{ 9}}\,C$
Solution
Here, distance of point from the centre of the
sphere, $\mathrm{r}=20 \mathrm{\,cm}=0.2 \mathrm{\,m}$
Electric field, $\mathrm{E}=-1.2 \times 10^{3} \mathrm{\,N} \mathrm{C}^{-1}$
As $\mathrm{E}=\frac{\mathrm{q}}{4 \pi \varepsilon_{0} \mathrm{r}^{2}}$
$\therefore $ $\mathrm{q}=\left(4 \pi \varepsilon_{0}^{2}\right) \mathrm{E}=\frac{(0.2)^{2} \times\left(-1.2 \times 10^{3}\right)}{9 \times 10^{9}}$
$=-5.3 \times 10^{-9} \mathrm{\,C}$
