Using Biot-Savart law, derive expression for the magnetic field $(B)$ due to a circular current carrying loop at a point on its axis and hence at its centre.

An electron moving with a velocity $\vec{v}=\left(1.0 \times 10^7\right.$ $\mathrm{m} / \mathrm{s}) \hat{i}+\left(0.5 \times 10^7 \mathrm{~m} / \mathrm{s}\right) \hat{j}$ enters a region of uniform magnetic field $\vec{B}=(0.5 \mathrm{mT}) \hat{j}$. Find the radius of the circular path described by it. While rotating; does the electron trace a linear path too? If so, calculate the linear distance covered by it during the period of one revolution.