Question

$4\times 10^{10}$ electrons are removed from a neutral metal sphere of diameter $20 \, c m$ placed in air. The magnitude of the electric field in $\left(\right. N \left( \, C\right)^{- 1} \left.\right)$ at a distance of $20 \, c m$ 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 $\left(D\right)=20 \, cm$
Radius of sphere $\left(r\right)=\frac{20}{2}=10 \, cm=0.01 \, m$
According to equation,
$E_{o u t s i d e}=\frac{q}{4 \pi \epsilon _{0} r^{2}}$
$=\frac{n e}{4 \pi \epsilon _{0} r^{2}}$
Here, $r=20\times 10^{- 2}m$
$=\frac{4 \times \left(10\right)^{10} \times 1.6 \times \left(10\right)^{- 19} \times 9 \times \left(10\right)^{9}}{\left(20 \times \left(10\right)^{- 2}\right)^{2}}$
$=\frac{4 \times 1.6 \times 9}{20 \times 20 \times 10^{- 4}}$
$=\frac{4 \times 1.6 \times 9 \times 10^{4}}{20 \times 20}$
$=1.6\times 9\times 10^{2}$
$=1.44\times 10^{3}=1440NC^{- 1}$