Question

A cylindrical air capacitor has two concentric rings, having inner radius $4cm$ and outer radius $7cm$. The capacitance per unit length is 994$\times {10}^{-x}$. Find the value of $x.$

Answer 1

Solution:
The cylindrical air capacitors have two concentric rings.
The inner radius $a=4$ cm.
The outer radius $b=7$ cm.
Given Capacitance per unit length = $994\times {10}^{-}x$
$\pi =3.14$
$ϵ=8.854\times {10}^{-}12$ F/m
$k=1$
Let the constant in the formula
= $2\times \pi \times ϵ\times k$
=$2\times 3.14\times 8.854\times {10}^{-}12\times 1$
= $55.603\times {10}^{-}12$
According to the formula
$\frac{C}{L}$= $\frac{constant}{\ln \left(\frac{b}{a}\right)}$= $\frac{55.603\times {10}^{-}12}{\ln \left(\frac{7}{4}\right)}$=$99.3952\times {10}^{-}12$
Hence, $x=11$