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

Current density `j=(1)/(pia^(2))`
form ampere 's circuital law
`int B.dl=mu.I_("enclosed")`
for `rgta`
`Bxx2pir=mu_(0)l rarr B=(mu_(0)l)/(2pir)`
At r=2a , `B_(2)=(mu_(0)I)/(4piA)`
So `(B_(1))/(B_(2))=1`