A spherical valume contains a unifromly distributed charge of density `1.0xx10^(-6)C//m^(3)`. Find the electrical field (in N/C) at a point inside the volume at a distance 1 mm from the centre. `("Let "(1)/(4piin_(0))=9xx10^(9)Nm^(2)C^(-2))`

Options

A. `(8)/(pi)`
B. `6pi`
C. `(pi)/(6)`
D. `12pi`

Answer

D

Explanation

Given the volume charge density of sphere,
`rho_(v)=1xx10^(-6)C//m^(3)`
`(1)/(4piepsi_(0))=9xx10^(9)Nm^(2)C^(-2)`
r=1 mm `=10^(-3)` m
Charge on sphere,
q=charge density `xx` volume
`=rho_(v)xx(4)/(3)pr^(3)" "("":'V=(4)/(3)pir^(2))`
`:.` Electric field intersity at a distance, r,
`E=(1)/(4piepsi_(0)).(q)/(r^(2))`
`E=(1)/(4piepsi_(0)).(rho_(v)xx(4)/(3)pir^(3))/(r^(2)).(rho_(v)xx4pir)/(3)`
`E=12pi`
Hence, the electric field inside the sphere at a distance 1 mm from the centre is `12pi` N/C.