Current Loop as a Magnetic Dipole

The magnetic moments associated with two closely wound circular coils a and b of radius $r$ and $2r$ respectively are equal if (where $N_a, I_a$ and $N_b, I_b$ are number of turns and current in A and B respectively)

A particle of charge '$q$' and mass '$m$' moves in a circular orbit of radius '$r$' with angular speed '$\omega$'. The ratio of the magnitude of its magnetic moment to that of its angular momentum depends upon

A rectangular coil of $n$ turns has area $\vec{A}$ and it is placed in uniform magnetic field $\vec{B}$. If the current passing through the coil is 'I' then the torque acting on the coil is

Torque acting on a coil carrying current 'I' situated parallel to magnetic field of induction 'B' having of turns 'n' and area 'A' is

A uniform conducting wire of length $\text{'}12a\text{'}$ and resistance $R$ is wound up as a current carrying coil in the shape of an equilateral triangle of side $\text{'}a\text{'}$ and then a square of side $\text{'}a\text{'}$. The ratio of magnetic dipole moments of triangular to square coil is

A thin circular wire carrying current $I$ has magnetic moment $M$. The shape of the wire is changed to a square and it carries the same current. It will have magnetic moment $M_1$. The ratio $M$ to $M_1$ is

The ratio of magnetic field at the centre of the current carrying circular loop and its magnetic moment is '$x$'. When both the current and radius are tripled, then the ratio will be

Two wires of same length are bent to form the circular loop with two turns and a square loop of one turn. Both of them carry same current. The ratio of magnetic moment of circular loop of two turns to that of square loop is

A circular coil of 'N' turns and diameter 'd' carries current 'I'. It is unwound and rewound to make another coil of diameter '2d', current 'I' remaining the Same. The ratio of magnetic moments of the new coil to the original coil is

The magnetic flux near the axis and inside the air core solenoid of length 60 cm carrying current I is $\frac{\pi}{2} \times 10^{-6}$ Wb. Its magnetic moment will be (cross-sectional area is very small as compared to length of solenoid, $\mu_0$ = Permeability of free space = $4\pi \times 10^{-7}$ SI unit)

A circular coil of N turns and diameter D carries current I. It is unwound and rewound to make another coil of diameter 2D, current I remaining the same. The ratio of magnetic moments of the original coil to the new coil is

A 100-turn closely wound circular coil of radius 5 cm has a magnetic field of $3.14 \times 10^{-3}\text{ T}$ at its centre. The current flowing through the coil, and the magnitude of the magnetic moment of this coil are, respectively:

(Take $\mu_0 = 4\pi \times 10^{-7}\text{ T m/A}$)

The relation between magnetic moment (M) of revolving electron of charge (e) and mass (m) having principle quantum number (n) is (h = Planck's constant)

A wire of length $L$ is bent in the form of a circular coil and current '$i$' is passed through it. This coil is kept in magnetic field. The torque acting on the coil will be maximum, when the number of turns is ___

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 $B_o = 4 \times 10^{-3}\text{ T}$ and current $I = 100\sqrt{2}\text{ A}$, the torque experienced by the loop is ______ Wb.A. ( $\pi = 3.14$)

A circular coil of radius 2 cm and 125 turns carries a current of 1 A. The coil is placed in a uniform magnetic field of magnitude 0.4 T. The axis of the coil makes an angle of $30^\circ$ with the direction of the magnetic field. The torque acting on the coil is $\alpha \times 10^{-4}\text{ N.m}$. The value of $\alpha$ is $\rule{2em}{0.4pt}.\ (\pi = 3.14)$

A charge $q$ is circulating at a constant speed $v$ with a semicircular loop of radius $r$. The magnetic moment of this loop is

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

A 2 amp current is flowing through two different small circular copper coils having radii ratio $1 : 2$. The ratio of their respective magnetic moments will be

In hydrogen atom, an electron of charge 'e' revolves in an orbit of radius ' $r$ ' with speed ' $v$ '. The magnetic moment associated with electron is

Let the current ' $I$ ' be associated with an electron of charge ' $e$ ' moving in a circular orbit of radius ' $r$ ' with speed ' $v$ ' around the positively charged nucleus. The ratio $\frac{r}{v}$ is

The ratio of angular momentum $L$ of an electron to the magnetic dipole moment $\vec{m}$orb is ( ' $m$ ' is mass of electron, ' $e$ ' is charge on electron)

The relation between magnetic moment $(M)$ of a current carrying circular coil and length (L) of the wire used is

The magnetic field at the centre of a current carrying circular coil of area ' $A$ ' is ' $B$ '. The magnetic moment ( M) of the coil is ( $\mu_0 =$ permeability of free space)

A wire of length ' $L$ ' carries a current ' $I$ '. If the wire is turned into a square coil of single turn, the maximum magnitude of the torque in a given magnetic field $(\vec{B})$ is

Two wires of equal lengths are bent in the form of a square and a circular loop. They are suspended in a uniform magnetic field and same current is passed through them. Torque experienced by

Current $I$ is carried in a wire of length ' $L$ '. If wire is bent into a circular coil of single turn, the maximum torque in a given magnetic field $B$ is

Two similar wires of equal lengths are bent in the form of a square and a circular loop. They are suspended in a uniform magnetic field and same current is passed through them. Torque experienced by

A model for quantized motion of an electron in a uniform magnetic field $B$ states that the flux passing through the orbit of the electron is $n(h/e)$ where $n$ is an integer, $h$ is Planck's constant and $e$ is the magnitude of electron's charge. According to the model, the magnetic moment of an electron in its lowest energy state will be ( $m$ is the mass of the electron)

Magnetic induction produced at the centre of a circular loop of radius ' $R$ ' carrying a current is ' B '. The magnetic moment of the loop is ( $\mu_0 =$ permeability of free space)

Magnetic field at the centre of a circular loop of area ' $A$ ' is ' $B$ '. The magnetic moment of the loop will be

The magnetic flux near the axis and inside the air core solenoid of length 80 cm carrying current ' I ' is $1.57 \times 10^{-6}\text{ Wb}$. Its magnetic moment will be [cross-sectional area of a solenoid is very small as compared to its length, $\mu_0 = 4\pi \times 10^{-7}$ SI unit $](\pi = 3.14)$

A coil of ' $n$ ' turns and radius ' $R$ ' carries a current 'I'. It is unwound and rewound to make a new coil of radius $\frac{R}{3}$ and the same current is passed through it. The ratio of the magnetic moment of the new coil to that of the original coil is

The magnetic field at the centre of a current carrying circular coil of area ' $A$ ' is ' $B$ '. The magnetic moment of the coil is ( $\mu_0 =$ permeability of free space)

A straight magnetic strip has a magnetic moment of $44\text{ A m}^{2}$. If the strip is bent in a semicircular shape, its magnetic moment will be ________ $\text{A m}^{2}$.

(given $\pi = \frac{22}{7}$)

An electron is revolving in a circular orbit of radius $r$ in a hydrogen atom. The angular momentum of the electron is L. The relation between dipole moment (m) associated with it, gyromagnetic ratio ( R) and L is

A uniform magnetic field of $2 \times 10^{-3}\text{ T}$ acts along positive $Y$-direction. A rectangular loop of sides $20\text{ cm}$ and $10\text{ cm}$ with current of $5\text{ A}$ 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 coil having 100 turns, area of $5 \times 10^{-3}\text{ m}^{2}$, carrying current of $1\text{ mA}$ is placed in uniform magnetic field of $0.20\text{ T}$ such a way that plane of coil is perpendicular to the magnetic field. The work done in turning the coil through $90^\circ$ is _________ $\mu\text{J}$.

A circular coil having 200 turns, $2.5 \times 10^{-4}\text{ m}^{2}$ area and carrying $100\ \mu\text{A}$ current is placed in a uniform magnetic field of $1\text{ T}$. Initially the magnetic dipole moment $(\vec{M})$ was directed along $\vec{B}$. Amount of work, required to rotate the coil through $90^\circ$ from its initial orientation such that $\vec{M}$ becomes perpendicular to $\vec{B}$, is ________ $\mu$J.

The magnetic moment of a current (I) carrying circular coil of radius '$r$' and number of turns '$n$' depends on

The magnetic moments associated with two closely wound circular coils $A$ and $B$ of radius $r_A = 10\text{ cm}$ and $r_B = 20\text{ cm}$ respectively are equal if: (Where $N_A, I_A$ and $N_B, I_B$ are number of turns and current of $A$ and $B$ respectively)

A straight wire carrying a current (I) is turned into a circular loop. If the magnitude of the magnetic moment associated with it is '$M$', then the length of the wire will be

The ratio of magnetic field at the centre of the current carrying circular loop and magnetic moment is $X$. When both the current and radius are doubled, then the ratio will be

A coil of '$n$' turns and radius '$R$' carries a current '$I$'. It is unwound and rewound again to make another coil of radius $\left(\frac{R}{3}\right)$, current remaining the same. The ratio of magnetic moment of the new coil to that of original coil is

A solenoid of length $0.4\text{ m}$ and having 500 turns of wire carries a current $3\text{ A}$. A thin coil having 10 turns of wire and radius $0.1\text{ m}$ carries current $0.4\text{ A}$. the torque required to hold the coil in the middle of the solenoid with its axis perpendicular to the axis of the solenoid is $(\mu_0 = 4\pi \times 10^{-7}$ SI units, $\pi^{2} = 10)\ (\sin 90^\circ = 1)$

A wire of length $8\text{ m}$ is bent to form a circular loop in y-z plane. A current of $0.5\text{ A}$ is flowing in anticlockwise direction in it, the magnetic dipole moment of the loop is:

Two concentric circular loops of radii $r_1 = 30\text{ cm}$ and $r_2 = 50\text{ cm}$ are placed in $X - Y$ plane as shown in the figure. A current $I = 7\text{ A}$ 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 wire of length $314\text{ cm}$ carrying current of $14\text{ A}$ is bent to form a circle. The magnetic moment of the coil is ________ A $-\text{m}^{2}$. [Given $\pi = 3.14$]

A particle of charge 'q' and mass 'm' moves in a circular orbit of radius 'r' with angular speed '$\omega$'. The ratio of the magnitude of its magnetic moment to that of its angular momentum depends on

An electron in a circular orbit of radius $0.05\text{ nm}$ performs $10^{16}$ revolutions/second. What is the magnetic moment due to the rotation of electron? $(e = 1.6 \times 10^{-19}\text{ C})$

Magnetic moment of revolving electron of charge (e) and mass (m) in terms of angular momentum (L) of electron is:

The relation between magnetic moment 'M' of revolving electron and principle quantum number 'n' is

If the charge to mass ratio of an electron is 'A' C/kg, then the gyromagnetic ratio of an orbital electron in C/kg is

A current carrying loop is placed in a uniform magnetic field. The torque acting on the loop does not depend upon

The magnetic flux near the axis and inside the air core solenoid of length $60\text{ cm}$ carrying current '$I$' is $1.57 \times 10^{-6}\text{ Wb}$. Its magnetic moment will be $[\mu_0 = 4\pi \times 10^{-7}$, SI unit and cross-sectional area is very small as compared to length of solenoid.]

The magnetic field at the centre of a current carrying circular coil of area 'A' is 'B'. The magnetic moment of the coil is ( $\mu_0 =$ permeability of free space)

A uniform conducting wire of length 24a and resistance R is wound up as a current carrying coil in the shape of an equilateral triangle of side 'a' and then in the form of a square of side 'a'. The coil is connected to a voltage source V0. The ratio of magnetic moment of the coils in case of equilateral triangle to that for square is 1: $\sqrt{y}$ where y is ..................

A coil in the shape of an equilateral triangle of side 10 cm lies in a vertical plane between the pole pieces of permanent magnet producing a horizontal magnetic field 20 mT. The torque acting on the coil when a current of 0.2 A is passed through it and its plane becomes parallel to the magnetic field will be $\sqrt{x} \times$ 10$-$5 Nm. The value of x is .................

A wire of length $L$ metre carrying a current of $I$ ampere is bent in the form of a circle. Its magnetic moment is

A galvanometer coil has 500 turns and each turn has an average area of 3 $\times$ 10–4 m2. If a torque of 1.5 Nm is required to keep this coil parallel to a magnetic field when a current of 0.5 A is flowing through it, the strength of the field (in T) is ______.

An electron $(e)$ is revolving in a circular orbit of radius $r$ in hydrogen atom. The angular momentum of the electron is ($M =$ magnetic dipole moment associated with it and $m =$ mass of electron)

A charged particle going around in a circle can be considered to be a current loop. A particle of mass m carrying charge q is moving in a plane with speed v under the influence of magnetic field $\vec{B}$. The magnetic moment of this moving particle:

A wire carrying current I is bent in the shape ABCDEFA as shown, where rectangle ABCDA and ADEFA are perpendicular to each other. If the sides of the rectangles are of lengths a and b, then the magnitude and direction of magnetic moment of the loop ABCDEFA is

A square loop of side 2$a$ and carrying current I is kept in xz plane with its centre at origin. A long wire carrying the same current I is placed parallel to z-axis and passing through point (0, b, 0), (b >> a). The magnitude of torque on the loop about z-axis will be:

A square loop of side 2$a$, and carrying current I, is kept in XZ plane with its centre at origin. A long wire carrying the same current I is placed parallel to the z-axis and passing through the point (0, b, 0), (b >> a). The magnitude of the torque on the loop about z-axis is given by:

A small circular loop of conducting wire has radius a and carries current I. It is placed in a uniform magnetic field B perpendicular to its plane such that when rotated slightly about its diameter and released, it starts performing simple harmonic motion of time period T. If the mass of the loop is m then:

A circular coil has moment of inertia 0.8 kg m2 around any diameter and is carrying current to produce a magnetic moment of 20 Am2. The coil is kept initially in a vertical position and it can rotate freely around a horizontal diameter. When a uniform magnetic field of 4 T is applied along the vertical,it starts rotating around its horizontal diameter. The angular speed the coil acquires after rotating by 60° will be:

In a hydrogen atom, an electron of charge $e$ revolves in a orbit of radius $r$ with speed $v$. Then, magnetic moment associated with electron is

Torque acting on a rectangular coil carrying current ' $i$ ' situated parallel to magnetic field of induction ' $B$ ', having number of turns ' $n$ ' and area ' $A$ ' is

A circular coil and a square coil is prepared from two identical metal wires and a current is passed through it. Ratio of magnetic dipole moment associated with circular coil to that of square coil is

A square loop is carrying a steady current I and the magnitude of its magnetic dipole moment is m. if this square loop is changed to a circular loop and it carries the same current, the magnitude of the magnetic dipole moment of circular loop will be:

A rectangular coil (Dimension 5 cm × 2.5 cm) with 100 turns, carrying a current of 3 A in the clock- wise direction is kept centered at the origin and in the X-Z plane. A magnetic field of 1 T is applied along X-axis. If the coil is tilted through 45° about Z-axis, then the torque on the coil is:

A circular coil having N turns and radius r carries a current I. It is held in the XZ plane in a magnetic field B$\hat{i}$. The torque on the coil due to the magnetic field is:

An insulating thin rod of length $l$ has a linear charge density $\rho(x) = \rho_0\frac{x}{l}$ on it. The rod is rotated about an axis passing through the origin (x = 0) and perpendicular to the rod. If the rod makes n rotations per second, then the time averaged magnetic moment of the rod is -

A hoop and a solid cylinder of same mass and radius are made of a permanent magnetic material with their magnetic moment parallel to their respective axes. But the magnetic moment of hoop is twice of solid cylinder. They are placed in a uniform magnetic field in such a manner that their magnetic moments make a small angle with the field. If the oscillation periods of hoop and cylinder are Th and Tc respectively, then -

A charge q is spread uniformly over an insulated loop of radius r. If it is rotated with an angular velocity $\omega$ with resect to normal axis then the magnetic moment of the loop is:

The dipole moment of a circular loop carrying a current I, is m and the magnetic field at the centre of the loop is B1. When the dipole moment is doubled by keeping the current constant, the magnetic field at the centre of the loop is $B_2$. The ratio $\frac{B_1}{B_2}$ is:

A magnetic dipole in a constant magnetic field has:

A uniform magnetic field B of 0.3 T is along the positive Z-direction. A rectangular loop (abcd) of sides 10 cm × 5 cm carries a current I of 12 A. Out of the following different orientations which one corresponds to stable equilibrium?

A magnetic dipole is acted upon by two magnetic fields which are inclined to each other at an angle of 75°. One of the fields has a magnitude of 15 mT. The dipole attains stable equilibrium at an angle of 30° with this field. The magnitude of the other field (in mT) is close to

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

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

A closely wound solenoid of 2000 turns and area of cross-section 1.5 $\times$ 10$-$4 m2 carries a current of 2.0 A. It is suspended through its centre and perpendicular to its length, allowing it to turn in a horizontal plane in a uniform magnetic field 5 $\times$ 10 $-$2 tesla making an angle of 30° with the axis of the solenoid. The torque on the solenoid will be