A neutral sphere of radius r and density `rho` is placed in a uniform electric field E that exists on the earth's surface in the vertically upward direction. If atomic number and the mass number of the material of the sphere are Z and A respectively, then the fraction of electrons that should be removed from the sphere for it to remain in equilibrium is [Assume that the sphere is able to hold the necessary charge without any leakage. Here `N_(A)` - Avogadro number]

Options

A. `(2g)/(eEZAN_(A))`
B. `(3gA)/(eEZ)`
C. `(gA)/(eEZN_(A))`
D. `(2gA)/(eEZN_(A))`

Answer

C

Explanation

`mg=qE`
`mg=n e E`
`(4)/(3) pi r^(3) xx rho xx g = n e E`
`n=(4pi r^(3)rho g)/( 3eE)`
Number of moles of the metal in sphere `=(m)/(A)`
`=(4)/(3) (pi r^(3) rho)/(A)`
Number of metal atoms `=(4)/(3) (pi r^(3) rho xx N_(A))/(A)`
Total number of electrons `=(4)/(3) (pi r^(3) rho N_(A) xx Z)/(A) =N` Say
Required fraction `=(n)/(N)=(gA)/(eEZN_(A))`