Question

An infinite long straight conducting cylindrical shell of radius a is surrounded by a thin coaxial infinite conducting cylindrical shell of radius b. Assuming current flows uniformly through the cylindrical shell and returns through the outer shell, the inductance per unit length for this arrangement is

• A. $\frac{2{\mu }_0}{\pi }ln\left(\frac{b}{a}\right)$
  
• B. $\frac{{\mu }_0}{\pi }ln\left(\frac{b}{a}\right)$
  
• C. $\frac{{\mu }_0}{2\pi }ln\left(\frac{b}{a}\right)$
  
• D. $\frac{{\mu }_0}{4\pi }ln\left(\frac{b}{a}\right)$

Answer 1

The correct option is C

$\frac{{\mu }_0}{2\pi }ln\left(\frac{b}{a}\right)$

$\varphi ={\int }_a^b\frac{{\mu }_{0}i}{2\pi r}dr=\left[\frac{{\mu }_{0}i}{2\pi }ln\left(\frac{b}{a}\right)\right]i=Li\Rightarrow L=\frac{{\mu }_0}{2\pi }ln\left(\frac{b}{a}\right)$