Question

Calculate the inductance of a unit length of a double tape line as shown in figure. The tapes are separated by a distance $h$ which is considerably less than their width $b$.

• A. $\frac{{\mu }_{0}h}{b}$
• B. $\frac{{\mu }_{0}h}{2b}$
• C. $\frac{2{\mu }_{0}h}{b}$
• D. $\frac{\sqrt{2}{\mu }_{0}h}{b}$

Answer 1

The correct option is A $\frac{{\mu }_{0}h}{b}$

$\oint \overrightarrow{B}\cdot d\overrightarrow{l}={\mu }_{0}I\Rightarrow B.2b={\mu }_{0}I$
$\Rightarrow B=\frac{{\mu }_{0}I}{2b}\to$ due to one tape
Net field $=2B$
Magnetic flux passing through this double tape
$\varphi =2BA=2B\left(lh\right)\Rightarrow \varphi =\frac{{\mu }_{0}I}{b}lh$
$L=\frac{\varphi }{I}=\frac{{\mu }_{0}lh}{b}\Rightarrow \frac{L}{l}=\frac{{\mu }_{0}h}{b}$