Question

What is the net charge on a conducting sphere of radius $10cm$? Given that the electric field $15cm$ from the centre of the sphere is equal to $3\times 10^{3}N/C$ and is directed inward

• A. $-7.5\times 10^{-5}C$
• B. $-7.5\times 10^{-9}C$
• C. $-7.5\times 10^{-5}C$
• D. $-7.5\times 10^{-9}C$

Answer 1

Answer: (B)

Electric field, $E=\frac{1}{4\pi {\epsilon }_0}\frac{q}{r^2}3\times 10^3$
$=9\times 10^9\times \frac{q}{(15{)}^2\times 10^{-4}}$
$\therefore q=\frac{3\times 10^3\times 15\times 15\times 10^{-4}}{9\times 10^9}$
$q=75\times 10^{-10}$
$=7.5\times 10^{-9}N/C$
$q=-7.5\times 10^{-9}N/C$
Charge will be negative because direction of electric field towards the charge.