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. `1/2`
B. `1`
C. `4`
D. `1/4`

Answer

B

Explanation

Applying Ampere.s circuital law to loop 1, we get :
`B(2 pi a/2) = mu_(0) I/(pi a^(2)) xx (pi a^(2))/4 `
`rArr " " B = (mu_(0)I)/(4 pi a) `
For loop 2, we have :
`B. (2 pi (2a)) = mu_(0) I`
`rArr " " B. = (mu_(0)I)/(4 pi a) `
` :. " " B / (B . ) = 1`