Question

Consider a co-axial cable which 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 a current $l$ and outer shell carries an equal and opposite current.The magnetic field at a distance x from the axis where b<x<c is :

• A. $\frac{{\mu }_{o}I(c^2-b^2)}{2\pi x(c^2-a^2)}$
• B. $\frac{{\mu }_{o}I(c^2-x^2)}{2\pi x(c^2-a^2)}$
• C. $\frac{{\mu }_{o}I(c^2-x^2)}{2\pi x(c^2-b^2)}$
• D. zero

Answer 1

The correct option is C $\frac{{\mu }_{o}I(c^2-x^2)}{2\pi x(c^2-b^2)}$

$B_x=\frac{{\mu }_o}{2\pi }\frac{I_{in}}{x}$
where , $I_{in}=I-[\frac{I}{\pi (c^2-b^2)}\left]\right[\pi (x^2-b^2]$
$=\frac{I(c^2-x^2)}{(c^2-b^2)}$