Two metal spher4s having charge densities 5 `muC//m^2` and `-2muC//m^2` with radii 2 mm and 1 mm respectivly are kept in a hypothetical closed surface. Calculate total normal electric induction over the closed surface.

Explanation

Data: `sigma_(1)= 5 xx 10^(-6) C//m^(2), sigma_(2) = -2 xx 10^(-6) C//m^(2)`,
`r_(1) = 2 xx 10^(-3)m, r_(2) = 1 xx 10^(-3) m`
Surface charge density, `sigma = Q/A=Q/(4pir^(2))`
`therefore` The charges on the metal spheres are
`Q_(1) = sigma_(1)(4pir_(1)^(2))` and `Q_(2) = sigma_(2)(4pir_(2)^(2))`
By Gauss' theorem, the total normal electric induction over a closed surface is equal to the next charge enclosed.
`therefore` TNEI `=Q_(1) + Q_(2)=4pi(sigma_(1)r_(1)^(2) + sigma_(2)r_(2)^(2))`