Question

$1 \,g$ of cork with a charge $1\, \mu C$ floats motionless $1\, cm$ 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.,
$m g=F_{e}=Q E$
Now, electric field $E$ due to large plane is
$E=\frac{\sigma}{2 \varepsilon_{0}}$
$m g=\frac{\sigma}{2 \varepsilon_{0}} Q $
$\sigma=\frac{2 \varepsilon_{0} m g}{Q}=\frac{2 \times 8.85 \times 10^{-12} \times 10^{-3} \times 9.8}{1 \times 10^{-6}} $
$=17.3 \times 10^{-8} C / m ^{2}$