Question

$4\times 10^{10}$ electrons are removed from a neutral metal sphere of diameter $20cm$ placed in air. The magnitude of the electric field (in $N{C}^{-1}$ ) at a distance of $20cm$ from its centre is

• A. 5760
• B. 1440
• C. 640
• D. Zero

Answer 1

Answer: (B)

Given.
Number of electrons $(n)=4\times 10^{10}$
Diameter of sphere $(D)=20cm$
Radius of sphere $(r)=\frac{20}{2}=10cm=0.01m$
According to question,
$E_{\text{ourside }}=\frac{q}{4\pi {\epsilon }_0{r}^2}$
$=\frac{ne}{4\pi {\epsilon }_0{r}^2}$
Here, $r=20\times 10^{-2}m$
$=\frac{4\times 10^{10}\times 16\times 10^{-19}\times 9\times 10^9}{{\left(20\times 10^{-2}\right)}^2}$
$=\frac{4\times 1.6\times 9}{20\times 20\times 10^{-4}}$
$=\frac{4\times 1.6\times 9\times 10^4}{20\times 20}$
$=16\times 9\times 10^2$
$=1.44\times 10^2=1440N{C}^{-1}$