A cylindrical capacitor has two co-axial cylinders of length 15 cm and radial 1.5 and 1.4 cm.The outer cylinder is earthed and inner cylinder is given a charge of `3.5 muC`. 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 coaxial cylinder ,l=15 cm=0.15 cm
radius of outer cylinder , `r_(1)=1.5 cm =0.015 cm `
radius of inner cylinder , `r_(2)=1.4 cm =0.0014 m `
charge on the inner cylinder, `q=3.5 muC=3.5xx10^(-6)C`
Capacitance of a co-axial cylinder of radii `r_(1)` and `r_(2)` is given by the relation
`C=(2piin_(0)l)/(log((r_(1))/(r_(2)))`
Where `in_(0)`=permitivity of free space =`8.85xx10^(-12)N^(-1)m^(-2)C^(2)`
`:. C=(2pixx8.85xx10^(-12)xx0.15)/(2.3026 log_(10)(0.15/0.14))`
=`(2pixx8.85xx10^(-12)xx0.15)/(2.3026xx0.0299)=1.2xx10^(-10) F`
potential difference of the inner cylinder is given by
`V=q/C`
`=(3.5xx10^(-6))/(1.2xx10^(-10)) =2.92xx10^(4)V`