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A cylindrical capacitor has two co-axial...

A cylindrical capacitor has two co-axial cyclinders of length 15 cm and radil 1.5 and 1.4 cm.The outer cylinder is earthed and inner cyclinder 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.)

Text Solution

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Here `L = 15 cms = 15xx10^(-2) m. r_(a) = 1.4 cm = 1.4xx10^(-2)m, r_(b) = 1.5 cm = 1.5xx10^(-2)m`
`q = 3.5 muC = 3.5xx10^(-6)` coulomb, `C = ? , V = ?`
`C = (2pi in_(0) L)/(log_(e) ((r_(b))/(r_(a)))) = (2pi in _(0) L)/(2.3026 log_(10) ((r_(b))/(r_(a))))`
`:. C = (2pi xx 8.85xx10^(-12)xx15xx10^(-2))/(2.3026 log_(10) ((1.5xx10^(-2))/(1.4xx10^(-2))))` `= (2pi xx8.85xx15xx10^(-14))/(2.3026 [log_(10) 1.5 - log_(10) 1.4]) = 1.2xx10^(-10) farad`
As `V = (q)/(C) :. V = (3.5xx10^(-6))/(1.2xx10^(-10)) = 2.9xx10^(4) vol t`.
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