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

Explanation

Length of a co - axial cylinder L = 15 cm = 0.15 m
`q = 3.5 mu C = 3.5xx10^(-6) C `
Inner radius `r_(1)` = 1.4 cm = 0.014 m
Outer radius `r_(2)` =1.5 cm 0.015 m
Capacitance of a co -axial cylinder ,
`C= (2pi in_(0)L)/("In"b//a)=(4piin_(0)L)/(2"In" b//a)=(L)/("2kIn"b//a)`
`=(0.15)/(2xx9xx10^(9)xx2.303xx"log" (0.015)/(0.014))`
`=(0.15xx10^(-9))/(18xx2.303xx"log"1.07)`
`=(0.15xx10^(9))/(18xx2.303xx0.0298)`
`:. C = 1.2 xx10^(10)F`
and potential V `=(q)/(C) = (3.5xx10^(-6))/(1.2xx10^(-10))=2.9xx10^(4)` V