Question

Calculate the inductance per unit length of a double tape line as shown in the 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 $\frac{{\mu }_{0}h}{b}$


According to Ampere's law,

$\oint \overrightarrow{B}.\overrightarrow{d}r={\mu }_{0}I$

$\Rightarrow B(2b+2h)={\mu }_{0}I$

$\Rightarrow 2Bb={\mu }_{0}I\left[\text{Distance}h\text{is considerably less than}b\right]$

$\therefore B=\frac{{\mu }_{0}I}{2b}\left[\text{Due to one tape}\right]$

So, net magnetic field,

$B_{\text{net}}=2B=\frac{{\mu }_{0}I}{b}$

Further,

Magnetic flux passing through this double tape,

$\varphi =BA=B\left(lh\right)\Rightarrow \varphi =\frac{{\mu }_{0}I}{b}\left(lh\right)$

$\Rightarrow \frac{\varphi }{I}=\frac{{\mu }_{0}lh}{b}$

$\Rightarrow L=\frac{{\mu }_{0}lh}{b}$

$\Rightarrow \frac{L}{l}=\frac{{\mu }_{0}h}{b}$