A cylinderical capacitor has two co-axial cylinders of length 15 cm and radii 1.5cm and 1.4 cm . The outer cylinder is earthed and the inner cylinder is given a charge of `3.5muC`. Determine the capacitance of the system and the potential of the inner cylinder. Neglect end effets (i.e., bending of filed lines at the ends).

Explanation

Here `L = 15 cms = 15 xx 10^(-2) m`
`r_(a) = 1.4 cm = 1.4 xx 10^(-2) m`,
`r_(b) = 1.5 cm = 1.5 xx 10^(-2) m`
`q = 3.5 mu C = 3.5 xx 10^(-6)` coloumb, c = ?
V = ?
As `C = (2 pi epsilon_(0) L)/(log_(e) ((r_(b))/(r_(a))) = (2 pi epsilon_(0)L)/(2.3026 log_(10) ((r_(b))/(r_(a)))`
`:. C = (2 pi xx 8.85 xx 10^(-12) xx 15 xx 10^(-2))/(2.3026 log_(10) ((1.5 xx 10^(-2))/(1.4 xx 10^(-2))))`
`= (2 pi xx 8.85 xx 15 xx 10^(-14))/(2.3026 [log_(10) 1.5 log_(10) 1.4])`
`1.2 xx 10^(-10)` Farad
As `V = (q)/(C )`
`:. V = (3.5 xx 10^(-6))/(1.2 xx 10^(-10)) = 2.9 xx 10^(4)` volt.