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

`B_2pia/2=mu_01/(pia_2)((pia^2)/4)`
`B_1=(mu_0i)/(4pia)`…(i)
`B_2 2pi(2a)=mu_0i`
`B_2=(mu_0i)/(4pia)`….(ii)
`B_1/B_2=1`
OR
`B_"in"=mu_0/2 1/R^2. r`
`B_"out"=mu_0/2 1/r`
`B_"in"/B_"out"=(a//2)/a^2xx29=1`