A charged spherical conductor has a surface density of `0.07 C cm^(-2)`. When the charge is increased by `4.4 C`, the surface density changes to `0.084 C cm^(-2). Find the initial charge and capacitance of the spherical conductor.

A charged spherical conductor has a surface density of `0.07 C cm^(-2)

1.	A charged spherical conductor has a surface density of `0.07 C cm^(-2)`. When the charge is increased by `4.4 C`, the surface density changes to `0.084 C cm^(-2). Find the initial charge and capacitance of the spherical conductor.
Answer» Correct Answer - `22 C ; 5.56xx10^(-12) F` Here, `sigma_(1) = 0.07 C cm^(-2)` and `sigma_(2) = 0.084 C cm^(-2)`. Let `q` be the charge on the spherical conductor of radius `r` cm. `:. Sigma_(1) = (q)/(4pi r^(2)) = 0.07` …(i) and `sigma_(2) = (q + 4.4)/(4pi r^(2)) = 0.084` ….(ii) Dividing (ii) by (i), we get `(q+ 4.4)/(q) = (0.084)/(0.07) = 1.2` or `q = 22 C` From (i), `r = sqrt((q)/(4pi xx 0.07)) = sqrt((22xx7)/(4xx22xx0.07)) = 5cm` `r = 0.05m` `C = 4pi in_(0) r = (0.05)/(9xx10^(6)) = 5.56xx10^(-12) F`

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A charged spherical conductor has a surface density of `0.07 C cm^(-2)`. When the charge is increased by `4.4 C`, the surface density changes to `0.084 C cm^(-2). Find the initial charge and capacitance of the spherical conductor.

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