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 ${NC}^{-1}$) at a distance of $20cm$ from its center is :

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

Answer 1

Answer: (D)

$1440$

Charge of each electron $e=1.6\times {10}^{-19}C$

Number of electrons removed from the sphere $n=4\times {10}^{10}$

Thus total charged removed from the sphere $q=ne$

$\therefore$ $q=4\times {10}^{10}\times 1.6\times {10}^{-19}=6.4\times {10}^{-9}C$

Distance of point from the center of sphere $r=20cm=0.2m$

Thus electric field at that point $E=\frac{kq}{r^2}$ where $k=\frac{1}{4\pi {ϵ}_o}=9\times {10}^9$

$⟹$ $E=\frac{9\times {10}^9\times 6.4\times {10}^{-9}}{(0.2{)}^2}=1440N{C}^{-1}$