$ABCD$ 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

Find the magnetic field at point $P$ due to given arrangements of current carrying wire.

$\left(\mathrm{a}\right)$ 

$\left(\mathrm{b}\right)$

$\left(\mathrm{c}\right)$ 

$\left(\mathrm{d}\right)$ 

$\left(\mathrm{e}\right)$ 

Find magnetic field at point $P$ in following cases.

Find magnitude and direction of force on following current carrying wires. Direction of magnetic field has been indicated in each case.

Find instantaneous direction of force in following cases (magnetic field, velocity are indicated)

Two circular rings each of radius $\text{'}a\text{'}$ are joined together such that their planes are perpendicular to each other as shown in figure. (circle with solid line representation in vertical plane and the other circle with dotted line representation is horizontal plane respectively) A very small loop of mass $m$ and radius $r$ carrying a current $I_0$ is placed in the plane of the paper at common centre of each ring. The loop can freely rotate about any of its diametric axis. Find the time period (in s) of loop for small oscillations $\left(ma=\frac{2\pi {\mu }_0{I}_0}{{\pi }^2}\right)·$ Resistances of each half ring is shown in figure.

A charge $q,$ mass $m,$ travelling with speed $v$ enters a region of magnetic field at an angle $\theta$ with magnetic field. Mark the following statements as true or false.

$\left(\mathrm{a}\right)$ Kinetic energy of particle remains constant irrespective of $\theta$

$\left(\mathrm{b}\right)$ Velocity of particle remains constant if $\theta =n\pi ,$ where $n$ is an integer

$\left(\mathrm{c}\right)$ Speed of particle remains constant

$\left(\mathrm{d}\right)$ Acceleration of particle remains constant if $\theta =\left(2n-1\right)\frac{\pi }{2}$

$\left(\mathrm{e}\right)$ Average velocity of particle becomes negligible if $\theta =\left(2n-1\right)\frac{\pi }{2}$ over a long time