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)
$\frac{ B _{1}}{ B _{2}}=\frac{\mu_{ o } i _{ o } \frac{ x }{2 \pi a ^{2}}}{\frac{\mu_{0} i _{0}}{2 \pi x }}=\frac{ x ^{2}}{ a ^{2}}$