Question

A conducting sphere of radius $10\,cm$ has unknown charge. If the electric field at a distance $20\,cm$ from the centre of the sphere is $1.2 \times 10^3\, N\, C^{-1}$ and points radially inwards. The net charge on the sphere is

• A. $-4.5 \times 10^{-9}\, C$
• B. $4.5 \times 10^{9}\, C$
• C. $-5.3 \times 10^{-9}\, C$
• D. $5.3 \times 10^{9}\, C$

Answer 1

Answer: (C)

Here, distance of point from the centre of the sphere, $r = 20 \,cm = 0.2 \,m$
Electric field, $E = -1.2 \times 10^3\,N\, C^{-1}$
As $E=\frac{q}{4\pi\varepsilon_{0}r^{2}}$
$\therefore q=\left(4\pi\varepsilon_{0}r^{2}\right)E=\frac{\left(0.2\right)^{2}\times\left(-1.2\times10^{3}\right)}{9\times10^{9}}$
$=-5.3\times10^{-9}\,C$