`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

Options

A. `8.7xx10^(-8)C//m^(2)`
B. `17.3xx10^(-18)C//m^(2)`
C. Zero
D. `-1 mu C//m^(2)`

Answer

b

Explanation

The cork floats motionless if the weight of the cork is equal to electrostatic force due to uniformly charged plane of earth's surface
`mg= F_(e)= QE`
Since earth is considered as a conductor
`E=(sigma)/(2epsilon_(0))`
`mg= (sigma)/(2epsilon_(0))Q`
`sigma=(2epsilon_(0)mg)/(Q)=(2xx8.85xx10^(-12)xx10^(-3)xx9.8)/(1xx10^(-8))`
`= 17.3xx10^(-8)C//m^(2)`