An infinitely long uniform solid wire of radius $a$ carries a uniform dc current density $J$. The magnetic field at a distance $r$ from the center of the wire is proportional to

$r$ for $r<a$ and $1/r^2$ for $r>a$
$0$ for $r<a$ and $1/r$ for $r>a$
$r$ for $r<a$ and $1/r$ for $r>a$
$0$ for $r<a$ and $1/r^2$ for $r>a$

Correct answer: $r$ for $r<a$ and $1/r$ for $r>a$

Solution

For a uniform current density, the enclosed current inside radius $r<a$ is proportional to $r^2$, so Ampere's law gives $B\propto r$. Outside the wire, the enclosed current is constant, so $B\propto 1/r$.

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