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 $\frac{4}{3}M{L}^2$

If $r$ is the orbital radius and $v$ is the orbital velocity of an electron in a hydrogen atom, then its magnetic dipole moment is

A thin bar magnet of length $L$ and magnetic moment $M$ is bent at the midpoint so that the two parts are at right angles. The new magnetic length and magnetic moment are respectively

An $\mathrm{L}$ shaped bar magnet is converted into a straight bar magnet. It is found that the change in the magnetic moment is $40\%$. The original shape of the bar magnet was-

Here it is known to us that $y>x$. Later the shape of the bar magnet is like this

Calculate the ratio $\frac{y}{x}$.

The neutral points on the equatorial line were found to be at $0.2 \mathrm{m}$ from the centre of a short-bar magnet. The horizontal component of earths magnetic field induction is $0.39\times {10}^{-4}$Tesla. If ${\mu }_0=4\pi \times {10}^{-7}$ Henry/$\mathrm{m}$, the magnetic moment of the short-bar-magnet is

The intensity of magnetic field at a point $X$ on the axis of a small magnet is equal to the field intensity at another point $Y$ on equatorial axis. The ratio of distance of $X$ and $Y$ from the centre of the magnet will be

If the distance between two small bar magnets(treat as short dipole) is increased by $2\%$ Then force between them will decrease by

A square loop of side $a$ is made up of a metallic wire carrying a current $I$. The loop is kept perpendicular to a uniform magnetic field. Now the shape of the loop is changed from square to a circle without changing the length of the wire and current. The amount of work done in doing so is:

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?

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?

Following figures show the arrangement of bar magnets in different configurations. Each magnet has magnetic dipole $\overrightarrow{m}$. Which configuration has highest net magnetic dipole moment?

(a)(b)(C)(d)

Two identical bar magnets are fixed with their centres at a distance $\mathrm{d}$ apart. A stationary charge $\mathrm{Q}$ is placed at $P$ in between the gap of the two magnets at a distance $D$ form the center  $O$ as shown in the figure

The force on the charge is

A steel wire of length I has magnetic moment M. It is bent into a semi-circle. Now its magnetic moment is