Question

The electric field intensity at a distance of $20cm$ from the centre of a sphere is $10V/m$. The radius of the sphere is $5cm.$ Determine the electric field intensity at a point $8cm$ distance from the centre of the sphere.

Answer 1

Electric field intensity on any external point of sphere

$E=\frac{1}{4\pi {ϵ}_0}\frac{q}{r^2}$

According to question $r=20cm,=20\times {10}^{-2}m$

$E=10V/m$

$\therefore 10=9\times {10}^9\times \frac{q}{(20\times {10}^{[}-2{)}^2}$

$\therefore q=\frac{400\times {10}^{-4}\times 10}{9\times {10}^9}=4.4\times {10}^{-11}C$

now $r=8cm=8\times {10}^{-2}m$

$E=9\times {10}^9\times \frac{(4.4\times {10}^{-11})}{(8\times {10}^{-2}{)}^2}$

$=9\times {10}^9\times \frac{4.4\times {10}^{-11}}{64\times {10}^{-4}}=62.5V/m$