Question $13$

Consider a long $($practically infinite$)$ straight wire of radius, $\backslash ($ a $\backslash ),$ carrying a steady current that is uniformly distributed over its cross section as shown in the figure. Which of the following is FALSE?

$($a$)$ Cylindrical wire

$($b$)$ Wire cross section

The magnitude of the magnetic field intensity, $\backslash (\backslash$boldsymbol$\{$H$\}\backslash ),$ inside the wire is proportional to the distance, $\backslash ($ r$\_\{1\}\backslash ),$ from the wire axis.

The magnitude of the magnetic field intensity, $\backslash (\backslash$boldsymbol$\{$H$\}\backslash ),$ on the surface of the wire $\backslash (($r$=$a$)\backslash )$ is inversely proportional to $\backslash ($ a$^\{2\}\backslash ).$

The magnitude of the magnetic field intensity, $\backslash (\backslash$boldsymbol$\{$H$\}\backslash ),$ outside the wire is inversely proportional to the distance, $\backslash ($ r$\_\{2\}\backslash ),$ from the wire axis.

The magnitude of the magnetic field intensity, $\backslash (\backslash$boldsymbol$\{$H$\}\backslash ),$ outside the wire is proportional to the current, $\backslash (\backslash$boldsymbol$\{$I$\}\backslash ),$ on the wire.