Question

Three long concentric conducting cylindrical shells have radii $R,2R$ and $2\sqrt{2R}$. Inner and outer shells are connected to each other. The capacitance across middle and inner shells per unit length is:

• A. $\frac{\frac{1}{3}{ϵ}_0}{ln2}$
• B. $\frac{6\pi {ϵ}_0}{ln2}$
• C. $\frac{\pi {ϵ}_0}{2ln2}$
• D. $noneofthese$

Answer 1

The correct option is B $\frac{6\pi {ϵ}_0}{ln2}$

The equivalent structure is shown in figure. Here the capacitance between inner and middle cylinder is equal to equivalent capacitance when $C_1$ and $C_2$ are in parallel.
$C_1=\frac{2\pi {ϵ}_0}{ln\left(\frac{2R}{R}\right)}=\frac{2\pi {ϵ}_0}{ln2}$
$C_2=\frac{2\pi {ϵ}_0}{ln\left(\frac{2\sqrt{2}R}{2R}\right)}=\frac{4\pi {ϵ}_0}{ln2}$
$C_{eq}=C_1+C_2=\frac{2\pi {ϵ}_0}{ln2}+\frac{4\pi {ϵ}_0}{ln2}=\frac{6\pi {ϵ}_0}{ln2}$