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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 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» Solution :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 |
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