Question

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 magnetic field at $\frac{a}{2}$ and $2a$ from its axis is

Answer 1

For a point inside the solid cylinder,
$B_{ins}=\frac{{\mu }_{o}ir}{2\pi a^2}$
at $r=\frac{a}{2}{B}_1=\frac{{\mu }_{o}i}{4\pi a}$
For a point outside the solid cylinder
$B_{out}=\frac{{\mu }_{o}i}{2\pi r}$
At $r=2a{B}_2=\frac{{\mu }_{o}i}{4\pi a}\Rightarrow \frac{B_1}{B_2}=1$