A Gaussian surface contains two charged spherical conductors -A and B, having radii of 3 mm and 2 mm respectivley. If their respective surface charge densities are `10muC//m^(2) and -5muC//m^(2)`, then the total normal electric induction over the Gaussian surface will be

Options

A. `5.8xx10^(-10)C`
B. `7.8xx10^(-10)C`
C. `8.8xx10^(-10)C`
D. `3.8xx10^(-10)C`

Answer

C

Explanation

`sigma=(Q)/(A)" "therefore Q=sigmaA=sigmaxx4piR^(2)`
`therefore Q_(1)=sigma_(1)A_(1)=10xx10^(-6)xx4pixx9xx10^(-6)C`
`Q_(2)=sigma_(2)A_(2)=-5xx10^(-6)xx4pixx4xx10^(-6)C`
`therefore Q=Q_(1)-Q_(2)=10^(-12)[90-20]xx4pi`
`=280pixx10^(-12)=280xx(22)/(7)xx10^(-12)`
`=8.8xx10^(-10)C`
`therefore`T.N.E.I.=total charge enclosed`=8.8xx10^(-10)C`