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(A) Given: Length $l = 15\,cm = 0.15\,m$,inner radius $a = 1.4\,cm = 0.014\,m$,outer radius $b = 1.5\,cm = 0.015\,m$,charge $q = 3.5\,\mu C = 3.5 	im

Vedclass · Accepted Answer

$1.21 	imes 10^{-10}\,F, 2.89 	imes 10^4\,V$

Vedclass · Answer

(A) Given: Length $l = 15\,cm = 0.15\,m$,inner radius $a = 1.4\,cm = 0.014\,m$,outer radius $b = 1.5\,cm = 0.015\,m$,charge $q = 3.5\,\mu C = 3.5 	imes 10^{-6}\,C$.The capacitance of a cylindrical capacitor is given by $C = \frac{2\pi \epsilon_0 l}{\ln(b/a)} = \frac{2\pi \epsilon_0 l}{2.303 \log_{10}(b/a)}$.Substituting the values: $C = \frac{2 	imes 3.14159 	imes 8.854 	imes 10^{-12} 	imes 0.15}{2.303 	imes \log_{10}(1.5/1.4)} \approx \frac{8.345 	imes 10^{-12}}{2.303 	imes 0.0299} \approx 1.21 	imes 10^{-10}\,F$.The potential of the inner cylinder relative to the earthed outer cylinder is $V = \frac{q}{C}$.$V = \frac{3.5 	imes 10^{-6}}{1.21 	imes 10^{-10}} \approx 2.89 	imes 10^4\,V$.

$A$ cylindrical capacitor has two cylinders of radii $1.4\,cm$ and $1.5\,cm$ and length $15\,cm$. 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.

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