A long straight wire of radius a carries a steady current I. The current is uniformly distributed over its cross section. The ratio of the magntic fields B and B' at radii distance `(a)/(2) and 2a` respectively, from the axis of the wire is

Options

A. `(1)/(2)`
B. 1
C. 4
D. `(1)/(4)`

Explanation

Magnetic field B at radial distance `(a)/(2)` from the axis of the wire can be calculated using Ampere's circuit law as follows.
`Bxx2pi(a)/(2)=mu_(0)(1)/(pia^(2))xxpi((a)/(2))^(2) or,B=(mu_(0)I)/(4 pia)`
Similarly, the magnetic field B' at radial distance 2a is given by,
`B'xxpi2a= mu_(0)I or, B'=(mu_(0)I)/(4pi a) :. (B)/(B')=1`
The option B is correct.