Magnetic Dipole

The figure shows a  current-carrying square loop $ABCD$ of side $10 \mathrm{cm}$ and current $i=10 \mathrm{A}$. The magnetic moment $\overrightarrow{M}$ of the loop is

A rectangular coil PQ has $2n$ turns, an area $2a$ and carries a current $2I$, (refer figure). The plane of the coil is at $60^{\text{o}}$ to a horizontal uniform magnetic field of flux density $B$. The torque on the coil due to magnetic force is

A conducting ring of mass $2 \mathrm{kg}$ and radius $0.5 \mathrm{m}$ is placed on a smooth horizontal plane. The ring carries a current $i=4 \mathrm{A}$. A horizontal magnetic field $B=10 \mathrm{T}$ is switched on at time $t=0$ as shown in the figure. The initial angular acceleration of the ring will be

A cone made of insulating material has a total charge $\mathit{Q}$ spread uniformly over its sloping surface having a slant length $\mathit{L}$. The energy required to take a test charge $\mathit{q}$ from infinity to apex $\mathrm{A}$ of the cone will be
 

A nonconducting disc of radius $R$ is rotating about an axis, passing through its centre and perpendicular to its plane, with an angular velocity $\omega$. Charge $q$ is distributed uniformly over its surface. The magnetic moment of the disc is

A wire loop carrying current $i$ is placed in the $x-y$ plane as shown in the figure. If an external uniform magnetic field $\overrightarrow{B}=B\hat{\text{i}}$ is switched on, then the torque acting on the loop is

$Q$ charge is uniformly distributed over the curve surface of a right circular cone of semi-vertical angle $\theta$ and height $h$. The cone is uniformly rotated about its axis at angular velocity $\omega$. Calculate associated magnetic dipole moment. $(h>R)$

A square current carrying loop made of thin wire and having a mass m = 10g can rotate without friction with respect to the vertical axis $\mathrm{{\rm O}}{\mathrm{{\rm O}}}_1\text{,}$passing through the centre of the loop at right angles to two opposite sides of the loop. The loop is placed in a homogeneous magnetic field with an induction $\text{B}={\text{10}}^{-1}\text{T}$directed at right angles to the plane of the drawing. A current I = 2A is flowing in the loop. Find the period of small oscillations that the loop performs about its position of stable equilibrium.

   

A compass needle oscillates $20$ times per minute at a place where the dip is ${30}^{\mathrm{o}}$ and $30$ times per minute where the dip is ${60}^{\mathrm{o}}$. The ratio of total magnetic field due to the earth at two places respectively is $\frac{4}{\sqrt{x}}$. The value of $x$ is

A dipole having dipole moment $\overrightarrow{M}$ is placed in two magnetic fields of strengths $B_1$ and $B_2$ respectively. If dipole oscillates $60$ times in $20$ seconds in $B_1$ magnetic field and $60$ oscillations in $30$ seconds in $B_2$ magnetic field. Then find $\left(\frac{B_1}{B_2}\right)$

Find the magnetic dipole moment for the loop shown.

Find the magnetic dipole moment for the loop shown.

Current $i$ is flowing in the closed-loop wire $OPQRO$ as shown in the figure. Portion $OPQ$ is in $xz$ plane and $QRO$ is in $xy$-plane. The magnetic dipole moment of this system is

A bar magnet suspended by a horse hair lies in the magnetic meridian when there is no twist in the hair, On turning the upper end of the hair through $150°$ from the meridian the magnet is deflected through $30°$ form the meridian. Then the angle through which the upper end of the hair has to be twisted to deflect the magnet through $90°$ from the meridian is ,

The net dipole moment of the system as shown in the figure is

A uniform rigid ring of radius $r$ and unknown mass is placed on a non-conducting horizontal table-top where exists a uniform horizontal magnetic field of Induction $B$ as shown in figure. Now a current $I$ that is double that of minimum current required to flip over the ring is switched on in the coil.

A bar magnet of length $10 \mathrm{cm}$ and pole strength $20 \mathrm{A}-\mathrm{m}$ is deflected through $30°$ from the magnetic meridian. If earth's horizontal component field is $\frac{320}{4\pi }\mathrm{A} {\mathrm{m}}^{-1}$. The moment of the deflecting couple is

Current $i$ is flowing in a circular loop of radius $a$. If half of the circle is turned by angle $90°$, find the magnetic moment of the system:

The magnetic needle of a vibration magnetometer makes 12 oscillations per minute in the horizontal component of earth's magnetic field. When an external short bar magnet is placed at some distance along the axis of the needle in the same line, it makes 15 oscillations per minute. If the poles of the bar magnet are interchanged, the number of oscillations it makes per minute is $\sqrt{n}$. What is the value of $n$?

A magnetic needle suspended parallel to a magnetic field requires $\sqrt{3} \mathrm{J}$ of work to turn it through $60°$. The torque needed to maintain the needle in this position will be