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 $(N{\left(C\right)}^{-1})$ at a distance of $20cm$ from its centre is

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

Answer 1

Answer: (D)

Given,
Number of electrons $\left(n\right)=4\times {\left(10\right)}^{10}$ $m^{-3}$
Diameter of sphere $\left(D\right)=20cm$
Radius of sphere $\left(r\right)=\frac{20}{2}=10cm=0.01m$
According to equation,
$E_{outside}=\frac{q}{4\pi {ϵ}_0{r}^2}$
$=\frac{ne}{4\pi {ϵ}_0{r}^2}$
Here, $r=20\times 10^{-2}m$
$=\frac{4\times {\left(10\right)}^{10}\times 1.6\times {\left(10\right)}^{-19}\times 9\times {\left(10\right)}^9}{{\left(20\times {\left(10\right)}^{-2}\right)}^2}$
$=\frac{4\times 1.6\times 9}{20\times 20\times 10^{-4}}$
$=\frac{4\times 1.6\times 9\times 10^4}{20\times 20}$
$=1.6\times 9\times 10^2$
$=1.44\times 10^3=1440N{C}^{-1}$