Magnetic Effects of Curre question bank (Physics)

A $5$ mg particle carrying a charge of $5\pi\times 10^{-6}$ C is moving with velocity of $(3\hat{i}+2\hat{k})\times 10^{-2}$ m/s in a region having magnetic field $\vec{B} = 0.1\hat{k}$ Wb/m$^2$. It moves a distance of $\alpha$ meter along $\hat{k}$ when it completes $5$ revolutions. The value of $\alpha$ is ________.

A current carrying circular loop of radius $2$ cm with unit normal $\hat{n} = \dfrac{\hat{k}+\hat{i}}{\sqrt{2}}$ is placed in a magnetic field, $\vec{B} = B_0(3\hat{i}+2\hat{k})$. If $B_0 = 4\times 10^{-3}$ T and current $I=100\sqrt{2}$ A, the torque experienced by the loop is ________ Wb·A. ($\pi=3.14$)