Question

A cylindrical capacitor has two co-axial cylinders of length 20 cm and radii 1.5 cm and 1.6 cm. the outer cylinder is earthed and given cylinder is charged with 4 $\mu C$. The capacitance of the system is (neglect end effects)

• A. $2.8\times {10}^{-8}$ F
• B. $4.2\times {10}^{-14}$ F
• C. $1.7\times {10}^{-10}$ F
• D. $3.4\times {10}^{-12}$ F

Answer 1

The correct option is C $1.7\times {10}^{-10}$ F

Length of a co-axial cylinder, $l=20cm=0.2m$

Radius of outer cylinder, $r_1=1.6cm=0.016m$

Radius of inner cylinder, $r_2=1.5cm=0.015m$

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

Capacitance of the system, $C=\frac{2\pi {ϵ}_{0}l}{2.303lo{g}_{10}\frac{b}{a}}=\frac{2\times \pi \times 8.854\times {10}^{-12}\times 0.2}{2.303\times lo{g}_{10}\frac{0.016}{0.015}}=1.7\times {10}^{-10}F$

Hence, option $\left(C\right)$ is correct.