The magnetic field at the centre of a current carrying circular loop of radius $R$ is $16 \mu \mathrm{~T}$. The magnetic field at a distance $x=\sqrt{3} R$ on its axis from the centre is

$\_\_\_\_$ $\mu \mathrm{T}$.

Three long straight wires carrying current are arranged mutually parallel as shown in the figure. The force experienced by 15 cm length of wire $Q$ is $\_\_\_\_$ .

$ \left(\mu_{\mathrm{o}}=4 \pi \times 10^{-7} \mathrm{~T} . \mathrm{m} / \mathrm{A}\right) $

Two identical circular loops $P$ and $Q$ each of radius $r$ are lying in parallel planes such that they have common axis. The current through $P$ and $Q$ are $I$ and $4 I$ respectively in clockwise direction as seen from $O$. The net magnetic field at $O$ is :

The current passing through a conducting loop in the form of equilateral triangle of side $4 \sqrt{3} \mathrm{~cm}$ is 2 A . The magnetic field at its centroid is $\alpha \times 10^{-5} \mathrm{~T}$. The value of $\alpha$ is $\_\_\_\_$ .

(Given : $\mu_{\mathrm{o}}=4 \pi \times 10^{-7}$ SI units)

An infinitely long straight wire carrying current $I$ is bent in a planar shape as shown in the diagram. The radius of the circular part is $r$. The magnetic field at the centre $O$ of the circular loop is :

A current carrying solenoid is placed vertically and a particle of mass $m$ with charge $Q$ is released from rest. The particle moves along the axis of solenoid. If $g$ is acceleration due to gravity then the acceleration (a) of the charged particle will satisfy :

A current carrying circular loop of radius 2 cm with unit normal $\hat{n}=\frac{\hat{k}+\hat{i}}{\sqrt{2}}$ is placed in a magnetic field, $\vec{B}=B_o(3 \hat{i}+2 \hat{k})$. If $B_o=4 \times 10^{-3} \mathrm{~T}$ and current $I=100 \sqrt{2} \mathrm{~A}$, the torque experienced by the loop is $\_\_\_\_$ Wb.A. ( $\pi=3.14$ )

A current of 30 A each flows in opposite directions in two conducting wires, placed parallel to each other at a distance of 8 cm . The magnetic field at the mid point between the two wires is $\_\_\_\_$ $\mu \mathrm{T}$.

$ \left(\frac{\mu_{\mathrm{o}}}{4 \pi}=10^{-7} \mathrm{~N} / \mathrm{A}^2\right) $

A small cube of side 1 mm is placed at the centre of a circular loop of radius 10 cm carrying a current of 2 A . The magnetic energy stored inside the cube is $\alpha \times 10^{-14} \mathrm{~J}$. The value of $\alpha$ is $\_\_\_\_$ .

$ \left(\mu_{\mathrm{o}}=4 \pi \times 10^{-7} \mathrm{Tm} / \mathrm{A}, \pi=3.14\right) $

A particle of charge $q$ and mass $m$ is projected from origin with an initial velocity $\vec{v}=\left(\frac{v_0}{\sqrt{2}} \hat{x}+\frac{v_0}{\sqrt{2}} \hat{y}\right)$. There exists a uniform magnetic field $\vec{B}=B_0 \hat{z}$ and a space varying electric field $\vec{E}=E_{\mathrm{o}} \mathrm{e}^{-\lambda x} \hat{x}$ within the region $0 \leqslant x \leqslant L$. After travelling a distance such that $x$-coordinate has changed from $x=0$ to $x=L$, the change in the kinetic energy is $\_\_\_\_$ .

An insulated wire is wound so that it forms a flat coil with $N=200$ turns. The radius of the innermost turn is $r_1=3 \mathrm{~cm}$, and of the outermost turn $r_2=6 \mathrm{~cm}$. If 20 mA current flows in it then the magnetic moment will be $\alpha \times 10^{-2} \mathrm{~A} . \mathrm{m}^2$. The value of $\alpha$ is $\_\_\_\_$ .

A particle having charge $10^{-9}$ C moving in $x$-$y$ plane in fields of $0.4 \hat{j}$ N/C and $4 \times 10^{-3} \hat{k}$ T experiences a force of $(4 \hat{i} + 2 \hat{j}) \times 10^{-10}$ N. The velocity of the particle at that instant is _________ m/s.

Two identical long current carrying wires are bent into the shapes shown in the following figures. If the magnitude of magnetic fields at the centres P and Q of a semicircular arc are $B_1$ and $B_2$ respectively, then the ratio $\frac{B_1}{B_2}$ is ______.

Figure shows a current carrying square loop ABCD of edge length is ‘a’ lying in a plane. If the resistance of the ABC part is r and that of ADC part is 2r, then the magnitude of the resultant magnetic field at centre of the square loop is

A particle of charge $q$, mass $m$ and kinetic energy $E$ enters in magnetic field perpendicular to its velocity and undergoes a circular arc of radius (r). Which of the following curves represents the variation of $r$ with $E$ ?

Uniform magnetic fields of different strengths $\left(B_1\right.$ and $\left.B_2\right)$, both normal to the plane of the paper exist as shown in the figure. A charged particle of mass $m$ and charge $q$, at the interface at an instant, moves into the region 2 with velocity $v$ and returns to the interface. It continues to move into region 1 and finally reaches the interface. What is the displacement of the particle during this movement along the interface?

(Consider the velocity of the particle to be normal to the magnetic field and $\mathrm{B}_2>\mathrm{B}_1$ )

Given below are two statements: one is labelled as $\mathbf{A s s e r t i o n} \mathbf{A}$ and the other is labelled as Reason $\mathbf{R}$

Assertion A : If Oxygen ion $\left(\mathrm{O}^{-2}\right)$ and Hydrogen ion $\left(\mathrm{H}^{+}\right)$enter normal to the magnetic field with equal momentum, then the path of $\mathrm{O}^{-2}$ ion has a smaller curvature than that of $\mathrm{H}^{+}$.

Reason R : A proton with same linear momentum as an electron will form a path of smaller radius of curvature on entering a uniform magnetic field perpendicularly.

In the light of the above statements, choose the correct answer from the options given below

In a moving coil galvanometer, two moving coils $\mathrm{M}_1$ and $\mathrm{M}_2$ have the following particulars :

$ \begin{aligned} & \mathrm{R}_1=5 \Omega, \mathrm{~N}_1=15, \mathrm{~A}_1=3.6 \times 10^{-3} \mathrm{~m}^2, \mathrm{~B}_1=0.25 \mathrm{~T} \\ & \mathrm{R}_2=7 \Omega, \mathrm{~N}_2=21, \mathrm{~A}_2=1.8 \times 10^{-3} \mathrm{~m}^2, \mathrm{~B}_2=0.50 \mathrm{~T} \end{aligned} $

Assuming that torsional constant of the springs are same for both coils, what will be the ratio of voltage sensitivity of $M_1$ and $M_2$ ?

Let $B_1$ be the magnitude of magnetic field at center of a circular coil of radius $R$ carrying current I. Let $\mathrm{B}_2$ be the magnitude of magnetic field at an axial distance ' $x$ ' from the center. For $x: \mathrm{R}=3: 4, \frac{\mathrm{~B}_2}{\mathrm{~B}_1}$ is :

Consider a long straight wire of a circular cross-section (radius a) carrying a steady current I. The current is uniformly distributed across this cross-section. The distances from the centre of the wire’s cross-section at which the magnetic field [inside the wire, outside the wire] is half of the maximum possible magnetic field, any where due to the wire, will be :

An infinite wire has a circular bend of radius a, and carrying a current I as shown in the figure. The magnitude of magnetic field at the origin O of the arc is given by:

Consider a long thin conducting wire carrying a uniform current I. A particle having mass "M" and charge " $q$ " is released at a distance " $a$ " from the wire with a speed $v_0$ along the direction of current in the wire. The particle gets attracted to the wire due to magnetic force. The particle turns round when it is at distance $x$ from the wire. The value of $x$ is [ $\mu_0$ is vacuum permeability]

N equally spaced charges each of value q , are placed on a circle of radius R . The circle rotates about its axis with an angular velocity $\omega$ as shown in the figure. A bigger Amperian loop B encloses the whole circle where as a smaller Amperian loop A encloses a small segment. The difference between enclosed currents, $I_A-I_B$, for the given Amperian loops is

Given below are two statements. One is labelled as Assertion (A) and the other is labelled as Reason (R).

Assertion (A) : A electron in a certain region of uniform magnetic field is moving with constant velocity in a straight line path.

Reason (R) : The magnetic field in that region is along the direction of velocity of the electron. In the light of the above statements, choose the correct answer from the options given below :

A long straight wire of a circular cross-section with radius ' a ' carries a steady current I . The current I is uniformly distributed across this cross-section. The plot of magnitude of magnetic field B with distance $r$ from the centre of the wire is given by

An electron projected perpendicular to a uniform magnetic field B moves in a circle. If Bohr's quantization is applicable, then the radius of the electronic orbit in the first excited state is :

A proton and a deutron $(q=+\mathrm{e}, m=2.0 \mathrm{u})$ having same kinetic energies enter a region of uniform magnetic field $\vec{B}$, moving perpendicular to $\vec{B}$. The ratio of the radius $r_d$ of deutron path to the radius $r_p$ of the proton path is:

Given below are two statements :

Statement (I) : When currents vary with time, Newton's third law is valid only if momentum carried by the electromagnetic field is taken into account

Statement (II) : Ampere's circuital law does not depend on Biot-Savart's law.

In the light of the above statements, choose the correct answer from the options given below :

A long straight wire of radius a carries a steady current I. The current is uniformly distributed across its cross section. The ratio of the magnetic field at $\frac{a}{2}$ and $2 a$ from axis of the wire is :

An element $\Delta l=\Delta x\hat{i}$ is placed at the origin and carries a large current $I=10 \mathrm{~A}$. The magnetic field on the $y$-axis at a distance of $0.5 \mathrm{~m}$ from the elements $\Delta x$ of $1 \mathrm{~cm}$ length is:

The electrostatic force $\left(\vec{F_1}\right)$ and magnetic force $\left(\vec{F}_2\right)$ acting on a charge $q$ moving with velocity $v$ can be written :

An electron is projected with uniform velocity along the axis inside a current carrying long solenoid. Then :

A uniform magnetic field of $2 \times 10^{-3} \mathrm{~T}$ acts along positive $Y$-direction. A rectangular loop of sides $20 \mathrm{~cm}$ and $10 \mathrm{~cm}$ with current of $5 \mathrm{~A}$ is in $Y-Z$ plane. The current is in anticlockwise sense with reference to negative $X$ axis. Magnitude and direction of the torque is:

A rigid wire consists of a semicircular portion of radius $R$ and two straight sections. The wire is partially immerged in a perpendicular magnetic field $B=B_0 \hat{k}$ as shown in figure. The magnetic force on the wire if it has a current $i$ is:

Two insulated circular loop A and B of radius '$a$' carrying a current of '$\mathrm{I}$' in the anti clockwise direction as shown in the figure. The magnitude of the magnetic induction at the centre will be :

Two particles $X$ and $Y$ having equal charges are being accelerated through the same potential difference. Thereafter they enter normally in a region of uniform magnetic field and describes circular paths of radii $R_1$ and $R_2$ respectively. The mass ratio of $X$ and $Y$ is :

A proton moving with a constant velocity passes through a region of space without any change in its velocity. If $\overrightarrow{\mathrm{E}}$ and $\overrightarrow{\mathrm{B}}$ represent the electric and magnetic fields respectively, then the region of space may have :

(A) $\mathrm{E}=0, \mathrm{~B}=0$

(B) $\mathrm{E}=0, \mathrm{~B} \neq 0$

(C) $\mathrm{E} \neq 0, \mathrm{~B}=0$

(D) $\mathrm{E} \neq 0, \mathrm{~B} \neq 0$

Choose the most appropriate answer from the options given below :

An electron is moving along the positive $\mathrm{x}$-axis. If the uniform magnetic field is applied parallel to the negative z-axis, then

A. The electron will experience magnetic force along positive y-axis

B. The electron will experience magnetic force along negative y-axis

C. The electron will not experience any force in magnetic field

D. The electron will continue to move along the positive $\mathrm{x}$-axis

E. The electron will move along circular path in magnetic field

Choose the correct answer from the options given below:

The source of time varying magnetic field may be

(A) a permanent magnet

(B) an electric field changing linearly with time

(C) direct current

(D) a decelerating charge particle

(E) an antenna fed with a digital signal

Choose the correct answer from the options given below:

An electron is allowed to move with constant velocity along the axis of current carrying straight solenoid.

A. The electron will experience magnetic force along the axis of the solenoid.

B. The electron will not experience magnetic force.

C. The electron will continue to move along the axis of the solenoid.

D. The electron will be accelerated along the axis of the solenoid.

E. The electron will follow parabolic path-inside the solenoid.

Choose the correct answer from the options given below:

A charge particle moving in magnetic field B, has the components of velocity along B as well as perpendicular to B. The path of the charge particle will be

A long straight wire of circular cross-section (radius a) is carrying steady current I. The current I is uniformly distributed across this cross-section. The magnetic field is

As shown in the figure, a long straight conductor with semicircular arc of radius $\frac{\pi}{10}$m is carrying current $\mathrm{I=3A}$. The magnitude of the magnetic field, at the center O of the arc is :

(The permeability of the vacuum $=4\pi\times10^{-7}~\mathrm{NA}^{-2}$)

Find the magnetic field at the point $\mathrm{P}$ in figure. The curved portion is a semicircle connected to two long straight wires.

A rod with circular cross-section area $2 \mathrm{~cm}^{2}$ and length $40 \mathrm{~cm}$ is wound uniformly with 400 turns of an insulated wire. If a current of $0.4 \mathrm{~A}$ flows in the wire windings, the total magnetic flux produced inside windings is $4 \pi \times 10^{-6} \mathrm{~Wb}$. The relative permeability of the rod is

(Given : Permeability of vacuum $\mu_{0}=4 \pi \times 10^{-7} \mathrm{NA}^{-2}$)

As shown in the figure, a current of $2 \mathrm{~A}$ flowing in an equilateral triangle of side $4 \sqrt{3} \mathrm{~cm}$. The magnetic field at the centroid $\mathrm{O}$ of the triangle is

(Neglect the effect of earth's magnetic field)

A current carrying rectangular loop PQRS is made of uniform wire. The length $P R=Q S=5 \mathrm{~cm}$ and $P Q=R S=100 \mathrm{~cm}$. If ammeter current reading changes from I to $2 I$, the ratio of magnetic forces per unit length on the wire $P Q$ due to wire $R S$ in the two cases respectively $\left(f_{P Q}^I: f_{P Q}^{2 t}\right)$ is:

A massless square loop, of wire of resistance $10 \Omega$, supporting a mass of $1 \mathrm{~g}$, hangs vertically with one of its sides in a uniform magnetic field of $10^{3} \mathrm{G}$, directed outwards in the shaded region. A dc voltage $\mathrm{V}$ is applied to the loop. For what value of $\mathrm{V}$, the magnetic force will exactly balance the weight of the supporting mass of $1 \mathrm{~g}$ ?

(If sides of the loop $=10 \mathrm{~cm}, \mathrm{~g}=10 \mathrm{~ms}^{-2}$)

The magnetic moments associated with two closely wound circular coils $\mathrm{A}$ and $\mathrm{B}$ of radius $\mathrm{r}_{\mathrm{A}}=10$ $\mathrm{cm}$ and $\mathrm{r}_{\mathrm{B}}=20 \mathrm{~cm}$ respectively are equal if : (Where $\mathrm{N}_{\mathrm{A}}, \mathrm{I}_{\mathrm{A}}$ and $\mathrm{N}_{\mathrm{B}}, \mathrm{I}_{\mathrm{B}}$ are number of turn and current of $\mathrm{A}$ and $\mathrm{B}$ respectively)

The electric current in a circular coil of four turns produces a magnetic induction 32 T at its centre. The coil is unwound and is rewound into a circular coil of single turn, the magnetic induction at the centre of the coil by the same current will be :

The magnitude of magnetic induction at mid point $\mathrm{O}$ due to current arrangement as shown in Fig will be

A single current carrying loop of wire carrying current I flowing in anticlockwise direction seen from +ve $\mathrm{z}$ direction and lying in $x y$ plane is shown in figure. The plot of $\hat{j}$ component of magnetic field (By) at a distance '$a$' (less than radius of the coil) and on $y z$ plane vs $z$ coordinate looks like

For a moving coil galvanometer, the deflection in the coil is 0.05 rad when a current of 10 mA is passes through it. If the torsional constant of suspension wire is $4.0\times10^{-5}\mathrm{N~m~rad^{-1}}$, the magnetic field is 0.01T and the number of turns in the coil is 200, the area of each turn (in cm$^2$) is :

Match List I with List II

	List I (Current configuration)		List II (Magnitude of Magnetic Field at point O)
A.		I.	${B_0} = {{{\mu _0}I} \over {4\pi r}}[\pi + 2]$
B.		II.	${B_0} = {{{\mu _0}} \over {4 }}{I \over r}$
C.		III.	${B_0} = {{{\mu _0}I} \over {2\pi r}}[\pi - 1]$
D.		IV.	${B_0} = {{{\mu _0}I} \over {4\pi r}}[\pi + 1]$

Choose the correct answer from the options given below :

A long solenoid is formed by winding 70 turns cm$^{-1}$. If 2.0 A current flows, then the magnetic field produced inside the solenoid is ____________ ($\mu_0=4\pi\times10^{-7}$ TmA$^{-1}$)

Two long straight wires P and Q carrying equal current 10A each were kept parallel to each other at 5 cm distance. Magnitude of magnetic force experienced by 10 cm length of wire P is F$_1$. If distance between wires is halved and currents on them are doubled, force F$_2$ on 10 cm length of wire P will be:

A circular loop of radius $r$ is carrying current I A. The ratio of magnetic field at the center of circular loop and at a distance r from the center of the loop on its axis is :

A wire X of length $50 \mathrm{~cm}$ carrying a current of $2 \mathrm{~A}$ is placed parallel to a long wire $\mathrm{Y}$ of length $5 \mathrm{~m}$. The wire $\mathrm{Y}$ carries a current of $3 \mathrm{~A}$. The distance between two wires is $5 \mathrm{~cm}$ and currents flow in the same direction. The force acting on the wire $\mathrm{Y}$ is

A triangular shaped wire carrying $10 \mathrm{~A}$ current is placed in a uniform magnetic field of $0.5 \mathrm{~T}$, as shown in figure. The magnetic force on segment $\mathrm{CD}$ is

(Given $\mathrm{BC}=\mathrm{CD}=\mathrm{BD}=5 \mathrm{~cm}$.)

The magnetic field at the center of current carrying circular loop is $B_{1}$. The magnetic field at a distance of $\sqrt{3}$ times radius of the given circular loop from the center on its axis is $B_{2}$. The value of $B_{1} / B_{2}$ will be

The current sensitivity of a galvanometer can be increased by :

(A) decreasing the number of turns

(B) increasing the magnetic field

(C) decreasing the area of the coil

(D) decreasing the torsional constant of the spring

Choose the most appropriate answer from the options given below :

As shown in the figure, a metallic rod of linear density $0.45 \mathrm{~kg} \mathrm{~m}^{-1}$ is lying horizontally on a smooth inclined plane which makes an angle of $45^{\circ}$ with the horizontal. The minimum current flowing in the rod required to keep it stationary, when $0.15 \mathrm{~T}$ magnetic field is acting on it in the vertical upward direction, will be :

{Use $g=10 \mathrm{~m} / \mathrm{s}^{2}$}

A cyclotron is used to accelerate protons. If the operating magnetic field is $1.0 \mathrm{~T}$ and the radius of the cyclotron 'dees' is $60 \mathrm{~cm}$, the kinetic energy of the accelerated protons in MeV will be :

$[\mathrm{use} \,\,\mathrm{m}_{\mathrm{p}}=1.6 \times 10^{-27} \mathrm{~kg}, \mathrm{e}=1.6 \times 10^{-19} \,\mathrm{C}$ ]

Two concentric circular loops of radii $r_{1}=30 \mathrm{~cm}$ and $r_{2}=50 \mathrm{~cm}$ are placed in $\mathrm{X}-\mathrm{Y}$ plane as shown in the figure. A current $I=7 \mathrm{~A}$ is flowing through them in the direction as shown in figure. The net magnetic moment of this system of two circular loops is approximately :

A charge particle is moving in a uniform magnetic field $(2 \hat{i}+3 \hat{j}) \,\mathrm{T}$. If it has an acceleration of $(\alpha \hat{i}-4 \hat{j})\, \mathrm{m} / \mathrm{s}^{2}$, then the value of $\alpha$ will be :

$\mathrm{B}_{X}$ and $\mathrm{B}_{\mathrm{Y}}$ are the magnetic fields at the centre of two coils $\mathrm{X}$ and $\mathrm{Y}$ respectively each carrying equal current. If coil $X$ has 200 turns and $20 \mathrm{~cm}$ radius and coil $Y$ has 400 turns and $20 \mathrm{~cm}$ radius, the ratio of $B_{X}$ and $B_{Y}$ is :

Two charged particles, having same kinetic energy, are allowed to pass through a uniform magnetic field perpendicular to the direction of motion. If the ratio of radii of their circular paths is $6: 5$ and their respective masses ratio is $9: 4$. Then, the ratio of their charges will be :

A coil of n number of turns wound tightly in the form of a spiral with inner and outer radii r₁ and r₂ respectively. When a current of strength I is passed through the coil, the magnetic field at its centre will be :

A cyclotron is working at a frequency of 10 MHz. If the radius of its dees is 60 cm. The maximum kinetic energy of accelerated proton will be :

(Take : e = 1.6 $\times$ 10^$-$19 C, m_p = 1.67 $\times$ 10^$-$27 kg)

Two long current carrying conductors are placed to each other at a distance of 8 cm between them. The magnitude of magnetic field produced at mid-point between the two conductors due to current flowing in them is 300 $\mu$T. The equal current flowing in the two conductors is :

Given below are two statements :

Statement I : The electric force changes the speed of the charged particle and hence changes its kinetic energy; whereas the magnetic force does not change the kinetic energy of the charged particle.

Statement II : The electric force accelerates the positively charged particle perpendicular to the direction of electric field. The magnetic force accelerates the moving charged particle along the direction of magnetic field.

In the light of the above statements, choose the most appropriate answer from the options given below :

A charge particle moves along circular path in a uniform magnetic field in a cyclotron. The kinetic energy of the charge particle increases to 4 times its initial value. What will be the ratio of new radius to the original radius of circular path of the charge particle :

Two parallel, long wires are kept 0.20 m apart in vacuum, each carrying current of x A in the same direction. If the force of attraction per meter of each wire is 2 $\times$ 10^$-$6 N, then the value of x is approximately :

An infinitely long hollow conducting cylinder with radius R carries a uniform current along its surface.

Choose the correct representation of magnetic field (B) as a function of radial distance (r) from the axis of cylinder.

Two long parallel conductors S₁ and S₂ are separated by a distance 10 cm and carrying currents of 4A and 2A respectively. The conductors are placed along x-axis in X-Y plane. There is a point P located between the conductors (as shown in figure).

A charge particle of 3$\pi$ coulomb is passing through the point P with velocity $\overrightarrow v = (2\widehat i + 3\widehat j)$ m/s; where $\widehat i$ and $\widehat j$ represents unit vector along x & y axis respectively.

The force acting on the charge particle is $4\pi \times {10^{ - 5}}( - x\widehat i + 2\widehat j)$ N. The value of x is :

A proton and an alpha particle of the same velocity enter in a uniform magnetic field which is acting perpendicular to their direction of motion. The ratio of the radii of the circular paths described by the alpha particle and proton is :

A long solenoid carrying a current produces a magnetic field B along its axis. If the current is doubled and the number of turns per cm is halved, the new value of magnetic field will be equal to

A long straight wire with a circular cross-section having radius R, is carrying a steady current I. The current I is uniformly distributed across this cross-section. Then the variation of magnetic field due to current I with distance r (r < R) from its centre will be :

A proton, a deutron and an $\alpha$-particle with same kinetic energy enter into a uniform magnetic field at right angle to magnetic field. The ratio of the radii of their respective circular paths is :

Given below are two statements : One is labelled as Assertion (A) and the other is labelled as Reason (R).

Assertion (A) : In an uniform magnetic field, speed and energy remains the same for a moving charged particle.

Reason (R) : Moving charged particle experiences magnetic force perpendicular to its direction of motion.

The magnetic field at the centre of a circular coil of radius r, due to current I flowing through it, is B. The magnetic field at a point along the axis at a distance ${r \over 2}$ from the centre is :

A rectangular loop of sides $10$ $cm$ and $5$ $cm$ carrying a current $1$ of $12A$ is placed in different orientations as shown in the figures below :

If there is a uniform magnetic field of $0.3$ $T$ in the positive $z$ direction, in which orientations the loop would be in $(i)$ stable equilibrium and $(ii)$ unstable equilibrium ?

Due to the presence of the current ${I_1}$ at the origin:

The magnitude of the magnetic field $(B)$ due to the loop $ABCD$ at the origin $(O)$ is :