Question

What is the net charge on a conducting sphere of radius $10\, cm$? Given that the electric field $15 \,cm$ 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, $E=\frac{1}{4 \pi \varepsilon_{0}} \frac{q}{r^{2}} 3 \times 10^{3}$
$=9 \times 10^{9} \times \frac{q}{(15)^{2} \times 10^{-4}}$
$\therefore q=\frac{3 \times 10^{3} \times 15 \times 15 \times 10^{-4}}{9 \times 10^{9}}$
$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.