Question

A coaxial cable consists of an inner wire of radius 'a' surrounded by an outer shell of inner and outer radii ' $b$ ' and ' $c$ ' respectively. The inner wire carries an electric current $i_0$, which is distributed uniformly across cross-sectional area. The outer shell carries an equal current in opposite direction and distributed uniformly. What will be the ratio of the magnetic field at a distance $x$ from the axis when (i) $x<a$ and (ii) $a<x<b$ ?

• A. $\frac{x^2}{a^2}$
• B. $\frac{a^2}{x^2}$
• C. $\frac{x^2}{b^2-a^2}$
• D. $\frac{b^2-a^2}{x^2}$

Answer 1

Answer: (A)

when $x<a$
$B_1(2\pi x)={\mu }_o\left(\frac{i_o}{\pi a^2}\right)\pi x^2$
$B(2\pi x)=\frac{{\mu }_0{i}_0{x}^2}{a^2}$
$B_1=\frac{{\mu }_o{i}_{o}x}{2\pi a^2}...$(1)
when $a<x<b$
$B_2(2\pi x)={\mu }_0{i}_0$
$B_2=\frac{{\mu }_0{i}_o}{2\pi x}....$(2)
$\frac{B_1}{B_2}=\frac{{\mu }_o{i}_o\frac{x}{2\pi a^2}}{\frac{{\mu }_0{i}_0}{2\pi x}}=\frac{x^2}{a^2}$