The wire consists of straight segments and a semicircular arc of radius $R$ carrying current $I$:

• The straight wire segments lie along lines passing through the centre $O$, so the angle between $d\vec{l}$ and $\vec{r}$ is $0^\circ$ or $180^\circ$, giving $B_{\text{straight}} = 0$.
• For a circular arc subtending angle $\theta$ at the centre, the magnetic field is:

For a semicircular arc, $\theta = \pi$ radians:

The centripetal force for circular motion in a magnetic field is provided by the magnetic Lorentz force:

The period of revolution is:

The frequency of revolution (cyclotron frequency) is:

Notice that the frequency depends only on charge $q$, magnetic field $B$, and mass $m$. It is completely independent of the speed $v$ and radius $r$. Hence, option 1 is the correct answer.

Analysis of the statements according to electromagnetic theory:

• Statement I is true: Electrostatic field $\vec{E}$ is produced by electric charge $q$, which is a scalar quantity obeying Coulomb's law: $d\vec{E} = \frac{1}{4\pi\varepsilon_0}\frac{dq}{r^2}\hat{r}$.
• Statement II is true: Magnetic field $\vec{B}$ is produced by a current element $I\,d\vec{l}$, which is intrinsically a vector quantity obeying the Biot-Savart law: $d\vec{B} = \frac{\mu_0}{4\pi}\frac{I(d\vec{l} \times \hat{r})}{r^2}$.