The Bar Magnet

The magnetic moment of a circular orbit of radius 'r' carrying a charge 'q' and rotating with velocity v is given by

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

The magnetic field lines due to a bar magnet are correctly shown in

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

Is it possible to isolate the poles of a magnet?

Magnetic poles exist in _____.

Inside a bar magnet, the magnetic field lines

$A$ thin bar magnet oscillates with a time period $T.$ If it is cut into two equal pieces along its axis, time period of oscillation of each piece is

The pole strength of poles of a bar magnet of effective length $0.1 \mathrm{m}$ is $40 \mathrm{A}-\mathrm{m}$. What is its magnetic moment in $\mathrm{A}-{\mathrm{m}}^2$?

A uniform magnetic field exists in space in the plane of paper and is initially directed from left to right. When a bar of soft iron is placed in the field parallel to it, the lines of force passing through it will be represented by:

Two lines of force due to a bar magnet:

Two identical magnetic dipoles of magnetic moment $1.0$ ${\mathrm{Am}}^2$ each are placed at a separation of $2 \mathrm{m}$ with their axes perpendicular to each other. The resultant magnetic field at a point midway between the dipoles is,

Inside a bar magnet, the magnetic lines of force

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