$A$ particle having a charge $50 \ e$ is revolving in a circular path of radius $0.4 \ m$ with $1 \ r.p.s.$ The magnetic field produced at the centre of the circle is $(\mu_0 = 4 \pi \times 10^{-7} \ SI \ units$ and $e = 1.6 \times 10^{-19} \ C)$.

$A$ rod with a circular cross-section area $2 \text{ cm}^2$ and length $40 \text{ cm}$ is wound uniformly with $400$ turns of an insulated wire. If a current $0.4 \text{ A}$ flows in the wire winding, the total magnetic flux produced inside the winding is $4\pi \times 10^{-6} \text{ Wb}$. The relative permeability of the rod is (Given permeability of vacuum $\mu_0 = 4\pi \times 10^{-7} \text{ N m A}^{-2}$)

The Biot-Savart law for a moving point charge $q$ with velocity $\vec{v}$ is given by $\vec{B} = \frac{\mu_0}{4\pi} \frac{q(\vec{v} \times \vec{r})}{r^3}$. This indicates that the magnetic field $\vec{B}$ produced by an electron moving with velocity $\vec{v}$ is such that:

Identify the correct statement.

Find the magnetic field at $P$ due to the arrangement shown.

Tesla is a unit for measuring