The number of electrons to be put on a spherical conductor of radius `0.1m` to produce an electric field of `0.036N//C` just above its surface is

Options

A. `2.4xx10^(5)`
B. `2.5xx10^(5)`
C. `2.6xx10^(5)`
D. `2.7xx10^(5)`

Answer

B

Explanation

The electric field at the surface of conductor
`E=1/(4piepsilon_(0)).q/(R^(2))`
Charge `q=4piepsilon_(0)R^(2)E`
From q=ne
`n e=4piepsilon_(0) R^(2)E`
`n=(4piepsilon_(0)R^(2)E)/e`
Here `4piepsilon_(0)=1/(9xx10^(9))` column `b^(2)//N-m^(2)`
R=0.1 m
E=0.036 N/C
`e=1.6xx10^(-19)` coulomb
So, `n=1/(9xx10^(9))xx((0.1)^(2)xx(0.036))/(1.6xx10^(-19))=2.5 xx10^(5)`