Question

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.

Answer 1

Given, `sigma_(1)=5 muC//m^2, sigma_(2)=-2muC//m^2, r_(1)=2mm,`
`r_(2)=1`mm.
Charge enclosed by each sphere,
`q_(1)=4pir_(1)^2xxsigma_(1)`
`q_(1)=4xx3*14(2xx10^(-3))^(2)xx5xx10^(-6)`
`q_(1)=4xx3*14xx20xx10^(-12)`
`q_(1)=251*2xx10^(-12)C`.
`q_(2)=4pir_2^2xxsigma=4xx3*14xx(10^(-3))^2xx(-2xx10^(-6))`
`q_(2)=-25*12xx10^(-12)C`.
According to the T.N.E.I. ( Total Normal Electrie Induction), ' it is equal to the total charge enclosed by that surface,'.
`"T.N.E.I." = Sigma_(q)+q_(2)`
`=251*2xx10^(-12)+(-25*12xx10^(-12))`
`=226*17xx10^(-12)Nn^2//C`