An electron (charge $-e,$ mass $m )$ enters a uniform magnetic field $\overrightarrow{B}=-B_0\hat{k}$ at $A$ with a speed $v_0$ at an angle $37°$ and leaves the field at $B$ with speed $v$ (see figure). Then choose the correct statement(s).

A rectangular loop carrying current $i$ is shown in the diagram. If the magnetic field in the region is $2B_0\hat{i}+B_0\widehat{ j},$ then choose the correct statement(s).

A circular loop of radius $R$ carries current $I$ and is parallel to the $x-y$ plane. A uniform external magnetic field $-B_0\hat{k}$ exists in the region. The maximum tension which the wire of the loop can withstand is $T_0.$ Then

A thick spherical shell with inner radius $2R$ and outer radius $4R$ has uniform charge density $\rho .$ The shell also has a spherical cavity of radius $R$ centered at $B.$ (see figure). Select the correct statement(s)

A thin insulated tightly wound wire forms a plane spiral of $N$ turns and carries current $I.$ The radii of inside and outside turns are a and $3a$ respectively. Then

$ABCD$ is a rigid square wire frame carrying a steady clockwise current $i$ with its centre at the origin. At time $t=0,$ the frame is at rest in the position shown in the figure. Each side of the frame is of mass $m$ and length $l.$ A uniform, constant magnetic field $B$ is directed at an angle of $45°$ to the $x$-axis in the $x-y$ plane. If the initial angular acceleration is $\frac{xBi}{12\mathrm{m}},$ the value of $x$ is