Question

$1g$ of cork with a charge $1\mu C$ floats motionless $1cm$ above a large uniformly charged plane near the surface of the earth. The surface charge density of the plane, assuming it to be an infinite sheet, is

• A. $8.7\times 10^{-8}C/m^2$
• B. $17.3\times 10^{-8}C/m^2$
• C. zero
• D. $-1\mu C/m^2$

Answer 1

Answer: (B)

The cork floats motionless if the weight of the cork is equal to electrostatic force due to uniformly charged plane near the earth's surface, i.e.,
$mg=F_e=QE$
Now, electric field $E$ due to large plane is
$E=\frac{\sigma }{2{\epsilon }_0}$
$mg=\frac{\sigma }{2{\epsilon }_0}Q$
$\sigma =\frac{2{\epsilon }_{0}mg}{Q}=\frac{2\times 8.85\times 10^{-12}\times 10^{-3}\times 9.8}{1\times 10^{-6}}$
$=17.3\times 10^{-8}C/m^2$