Question

$4 \times 10^{10}$ electrons are removed from a neutral metal sphere of diameter $20 \,cm$ placed in air. The magnitude of the electric field (in $NC^{-1}$ ) at a distance of $20 \,cm$ 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 $(D)=20 \,cm$
Radius of sphere $(r)=\frac{20}{2}=10 \,cm =0.01 \,m$
According to question,
$E_{\text {ourside }} =\frac{q}{4 \pi \varepsilon_{0} r^{2}} $
$=\frac{n e}{4 \pi \varepsilon_{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} $
$= 1.44 \times 10^{2}=1440\, NC ^{-1}$