2.32 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 μC. 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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alok kumar singh | Contributor-Level 10

4 months ago

2.32 Length of the co-axial cylinder, l = 15 cm = 0.15 m

Radius of the outer cylinder, $r_{1}$ = 1.5 cm = 0.015 m

Radius of the inner cylinder, $r_{2}$ = 1.4 cm = 0.014 m

Charge on the inner cylinder, q = 3.5 $μ C = 3.5 \times 10^{- 6}$ C

Capacitance of a co-axial cylinder of radii $r_{1}$ and $r_{2}$ is given by the relation

C = $\frac{2 π ε_{0} l}{\log_{e} ? \frac{r_{1}}{r_{2}}}$ , where $ε_{0}$ = permittivity of free space = 8.854 $\times 10^{- 12}$ $C^{2} N^{- 1}$ $m^{- 2}$

C = $\frac{2 π \times 8.854 \times 10^{- 12} \times 0.15}{\log_{e} ? \frac{0.015}{0.014}}$ = 1.21 $\times 10^{- 10}$ F

Potential difference of the inner cylinder is given by

V = $\frac{q}{C}$ = $\frac{3.5 \times 10^{- 6}}{1.21 \times 10^{- 10}}$ = 2.893 $\times 10^{4}$ V

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