Question

A conducting sphere of radius $10cm$ has unknown charge. If the electric field at a distance $20cm$ 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:

• A. $-4.5\times {10}^{-9}C$
• B. $4.5\times {10}^{9}C$
• C. $-5.3\times {10}^{-9}C$
• D. $5.3\times {10}^{9}C$

Answer 1

The correct option is C $-5.3\times {10}^{-9}C$

Here distance of the point from the centre of the sphere, $r=20cm=0.2m$
Electric field, $E=-1.2\times {10}^{3}N{C}^{-1}$

$E=\frac{q}{4\pi {\epsilon }_0{r}^2}$
$\therefore q=\left(4\pi {\epsilon }_0{r}^2\right)E=\frac{{\left(0.2\right)}^2\times (-1.2\times {10}^3)}{9\times {10}^9}=-5.3\times {10}^{-9}C$