A long, cylindrical wire of radius b carries a current i distributed uniformly over its cross section. Find the magnitude of the magnetic field at a point inside the wire at a distance a from the axis.

Options

A. `a=(R+r)/(2)`
B. `a=sqrt(Rr)`
C. `a=Rr//R+r`
D. `a=R^(2)//r`

Explanation

Applying Ampere's circuital law,
`B 2pir=(mu_(0)I pi r^(2))/(pia^(2))` for `r lt a`
and `B 2piR=mu_(0)I` for `R gt a`
Taking the ratio
`(r )/(R )=(r^(2))/(a^(2))`
`:. a=sqrt(Rr)`