A thin, hollow cylinder has infinite length and carries a uniform current that is circulating along its surface as shown. The current per unit length of the cylinder is $\lambda$. Which of the following are incorrect?

The cylinder is just like an ideal solenoid. Field inside an ideal solenoid is $B={\mu }_{0}ni$
Here, $ni=\lambda$
$\therefore$ Field inside the cylinder is $B={\mu }_0\lambda$
Field outside the cylinder is zero

Options (A), (C), (D) are wrong. Option (B) is correct.