If the capacitance per unit length of a cylindrical capacitor is 20 pF/m, what is the ratio of the radii of the two cylinders?
Answer & explanation
Correct answer: option 4
For a cylindrical capacitor, C = 2πεol/ln(R2/R1)
$\text{Capacitance per unit length is } \frac{C}{l} = \frac{2\pi \epsilon_0}{ln{\frac{R_2}{R_1}}} = 20\times 10^{-12}F/m$
$\Rightarrow ln{\frac{R_2}{R_1}} = \frac{2\pi \epsilon_0}{20\times 10^{-12}} = \frac{1}{18\times 10^9 \times 20\times 10^{-12}} = \frac{1}{0.36}= 2.77$
$\Rightarrow \frac{R_2}{R_1} = e^{2.77} = 16$
$\Rightarrow \frac{R_1}{R_2} = 1:16$