A positive, singly ionized atom of mass number $A_{\mathrm{M}}$ is accelerated from rest by the voltage $192 \mathrm{~V}$. Thereafter, it enters a rectangular region of width $w$ with magnetic field $\vec{B}_0=0.1 \hat{k}$ Tesla, as shown in the figure. The ion finally hits a detector at the distance $x$ below its starting trajectory.

[Given: Mass of neutron/proton $=(5 / 3) \times 10^{-27} \mathrm{~kg}$, charge of the electron $=1.6 \times 10^{-19} \mathrm{C}$.]

Which of the following option(s) is(are) correct?

Two concentric circular loops, one of radius R and the other of radius 2R, lie in the xy-plane with the origin as their common center, as shown in the figure. The smaller loop carries current I₁ in the anti-clockwise direction and the larger loop carries current I₂ in the clockwise direction, with I₂ > 2I₁. $$\overrightarrow B $$(x, y) denotes the magnetic field at a point (x, y) in the xy-plane. Which of the following statement(s) is(are) correct?

A long straight wire carries a current, I = 2 ampere. A semi-circular conducting rod is placed beside it on two conducting parallel rails of negligible resistance. Both the rails are parallel to the wire. The wire, the rod and the rails lie in the same horizontal plane, as shown in the figure. Two ends of the semi-circular rod are at the distances 1 cm and 4 cm from the wire. At time t = 0, the rod starts moving on the rails with a speed v = 3.0 m/s (see the figure).

A resistor R = 1.4 $$\Omega$$ and a capacitor C₀ = 5.0$$\mu$$F are connected in series between the rails. At time t = 0, C₀ is uncharged. Which of the following statement(s) is(are) correct? [$$\mu$$₀ = 4$$\pi$$ $$\times$$ 10^$$-$$7 SI units. Take ln 2 = 0.7]

Two infinitely long straight wires lie in the $$xy$$-plane along the lines $$x = \pm R.$$ The wire located at $$x = + R$$ carries a constant current $${I_1}$$ and the wire located at $$x=-R$$ carries a constant current $${I_2}.$$ A circular loop of radius $$R$$ is suspended with its center at $$\left( {0,0,\sqrt 3 R} \right)$$ and in a plane parallel to the $$xy$$-plane. This loop carries a constant current $$I$$ in the clockwise direction as seen from above the loop. The current in the wire is taken to be positive if it is in the $$ + \widehat j$$ direction. which of the following statements regarding the magnetic field $$\overrightarrow B $$ is (are) true?