A long straight wire of radius `a` carries a steady current `i`. The current is uniformly distributed across its cross section. The ratio of the magnetis field at `(a)//(2) and (2a)` is

Options

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

Answer

C

Explanation

At `r=a/2, B_(1)=(mu_(0)Ir)/(2pia^(2))=(mu_(0)I(a//2))/(2pia^(2))=(mu_(0)I)/(4pia)`
`r=2a, B_(2)=(mu_(0)I)/(2pir)=(mu_(0)I)/(4pia)`
`(B_(1))/(B_(2))=1`