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 magnetic fields `B` and `B'` , at radial distances `(a)/(2)` and `2a` respectively from the axis of the wire is:

Options

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

Answer

C

Explanation

Using Ampere circuit law
For points inside the wire
Loop-1
`B_(1) 2pi (a)/(2) = mu_(0) (I)/(pi a^(2)) xx (pi a^(2))/(4)`
`B_(1) = (mu_(0) I)/(4pi a)` ....(1)
Loop-2
`B_(2).2pi 2a = mu_(0) I`
`implies B_(2) = (mu_(0)I)/(4pi a)` .....(2)
`(B_(1))/(B_(2)) = 1`