Magnetic Dipole in External Magnetic Field

A uniform constant magnetic field $\overrightarrow{B}$ is directed at an angle of $45^{\text{o}}$ to the x-axis in the xy-plane, PQRS is a rigid square wire frame carrying a steady current $I_0$ (clockwise), with its centre at the origin O.  At time $t=0$, the frame is at rest in the figure, with its sides parallel to the x & y axes. Each side of the frame is at rest in the figure, with its centre at the origin Ο. Each side of the frame is of mass M & length L.
(1) What is torque $\overrightarrow{\tau }$ about Ο acting on the frame due to the magnetic field.
(2) Find the angle by which the frame rotate under the action of this torque in a short interval of time $\Delta t$, & the axis about which this rotation occurs ($\Delta t$ is so short that any variation in the torque during this interval may be neglected).

Given: Moment of inertia of the frame about an axis through its centre perpendicular to its plane is $\frac{4}{3}M{L}^2$

The length of a magnet is large compared to its width and breadth. The time period of its oscillation in a vibration magnetometer is $150 \mathrm{ms}$. The magnet is cut perpendicular to its length into three equal parts and three parts are then placed on each other with their like poles together. The time period of this combination (in $\mathrm{ms}$) will be

A magnet is placed in earth's magnetic field with north pole of the magnet pointing north. At the neutral point 

The work done in rotating a bar magnet of magnetic moment $\mathrm{M}$ from its unstable equilibrium position to its stable equilibrium position in a uniform magnetic field is $\mathrm{B}$is

Two magnetic are as shown in figure. Force between them is

The short bar magnetic are placed as shown in figure. The magnetic of force between them is proportional to

If two short bar magnetic are placing the line joining then as shown in the figure. Nature of force between two magnetic is

A short magnet produces a deflection of $30°$, when placed at certain distance, in $\tan A$ position of magnetometer. If another short magnet of double the length and thrice the pole strength, is placed at the same distance, in $\tan B$ position of the magnetometer, the deflection produced will be

A current carrying loop is placed in a uniform magnetic field in four different orientations. Arrange them in decreasing order of their potential energy.

(a) 

(b)

(c)

(d) 

A magnetic needle of magnetic moment $6.7\times {10}^{-2}\mathrm{ }\mathrm{A} {\mathrm{m}}^2$ and moment of inertia $7.5\times {10}^{-6} \mathrm{kg}\mathrm{ }{\mathrm{m}}^2$ is performing simple harmonic oscillations in a magnetic field of $0.01 \mathrm{T}$. Time taken for 10 complete oscillations is:

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

The length of a magnet is large compared to its width and breadth. The time period of its oscillation in a vibration magnetometer is $150 \mathrm{ms}$. The magnet is cut along its length into three equal parts and three parts are then placed on each other with their like poles together. The time period of this combination (in $\mathrm{ms}$) will be

An electron moves in a circular orbit with a uniform speed $v.$ It produces a magnetic field $B$ at the centre of the circle. The radius of the circle is proportional to :

A bar magnet of length $10 \mathrm{cm}$ and pole strength $2\mathrm{Am}$ is making an angle $60°$ with a uniform magnetic field of induction $50 T.$ Then the couple acting on it is ____ $\mathrm{Nm}$

At a neutral point

Two short bar magnets each of magnetic moment $9 {\mathrm{Am}}^2$ are placed such that one is at $x=-3 \mathrm{cm}$ and the other at $y=-3 \mathrm{cm}$. If their magnetic moments are directed along positive and negative $X$-directions respectively then the resultant magnetic field at the origin is

A bar magnet is placed at an angle of $30°$ to the direction of magnetic field induction of $5\times {10}^{-2} \mathrm{T}$ experiences a moment of couple $25\times {10}^{-6} \mathrm{N}-\mathrm{m}.$ If the length of magnet is $5 \mathrm{cm},$ its pole strength is $\dots \dots {10}^{-2} \mathrm{A}-\mathrm{m}.$

A magnet having time period $2$ oscillations/s at a place having magnetic field intensity of $0.4\times {10}^{-5} \mathrm{T}$. At another place, it takes $2 \mathrm{s}$ to complete one oscillation. The value of the earth's horizontal field at that place is $\frac{5}{\alpha }\times {10}^{-7} \mathrm{T}$. Write the value of $\alpha$.

A short bar magnet of magnetic moment $0.4 {\mathrm{JT}}^{–1}$  is placed in a uniform magnetic field of $0.16 \mathrm{T}.$ The magnet is in stable equilibrium when the potential energy is:

A conducting solid sphere having uniform charge $Q$ on it has radius $R$. It is rotating with an angular velocity $\omega$. If a uniform magnetic field $B$ is present perpendicular to axis of rotation then the torque on sphere will be