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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.)

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Answer Text

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

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