विद्युतचुंबकत्व

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:

An ammeter must measure total branch current with minimal resistance so as not to perturb the existing circuit current.

To convert a sensitive moving-coil galvanometer into an ammeter, a low resistance wire called a shunt ($S$) is connected in parallel with the galvanometer coil.

This shunt bypasses most of the large current while allowing only a small fraction $I_g$ to flow safely through the galvanometer coil. Hence, option 3 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: $d\vec{B} = \frac{\mu_0}{4\pi}\frac{I(d\vec{l} \times \hat{r})}{r^2}$.