A long cylinder of wire of radius 'a' carries a current i distributed uniformly over its cross section. If the magnetic fields at distances `rlta and Rgta` from the axis have equal magnitude, then

Options

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

Answer

B

Explanation

(b) Applying Ampere's circuital law.
`B2pir=(mu_0Ipir^2)/(pia^2)` for `r lt a`
and `B2piR=mu_0I` for `Rgta`
Taking the ratio
`r/R=(r^2)/(a^2) implies a=sqrt(Rr)`