Consider a coaxial 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 an electric current `i_0` and the outer shell carries an equal current in opposite direction. Find the magnetic field at a distance x from the axis where (a) `xlta,` (b) `altxltb`, (c) `bltxltc` and (d)`xgtc`. Assume that the current density is uniform in the inner wire and also uniform in the outer shell.

Options

A. for `x lt a,B=(mu_(0)Ix)/(2pia^(2))`
B. for `a lt x lt b,B=(mu_(0)I)/(2pix)`
C. for `b lt x lt c, B=(mu_(0)I(C^(2)-x^(2)))/(2pix(c^(2)-b^(2))`
D. all

Answer

D

Explanation

`x lt a, B=(mu_(0)Ix)/(2pia^(2))`
`a lt x lt b, B=(mu_(0)I)/(2pix)`
`b lt x lt c, Bxx2pix=mu_(0)[1-(I(x^(2)-b^(2)))/(pi(c^(2)-b^(2)))]`
`=(mu_(0)I)/(2pix) ((c^(2)-x^(2)))/((c^(2)-b^(2)))`