Question

A conducting sphere of radius $5\, cm$ has an unknown charge. The electric field at $10\, cm$ from the centre of the sphere is $1.8 \times 10^{3} N / C$ and points radially inward. What is the net charge on the sphere?

• A. $ 1.8\,\,nC $
• B. $ 2\,\,nC $
• C. $ 1\,\,nC $
• D. $ 1.5\,\,nC $

Answer 1

Answer: (B)

For a conducting charged sphere, the electric field outside the sphere
$(E)=\frac{1}{4 \pi \varepsilon_{0}} \frac{Q}{r^{2}}$
$1.8 \times 10^{3}=9 \times 10^{9} \times \frac{Q}{(0.1)^{2}}$
$Q=\frac{1.8 \times 10^{3} \times 10^{-2}}{9 \times 10^{9}}$
$=2 \times 10^{-9} C $
$=2 \,n C$