Magnetic Moment of a Current Loop

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

$Q$ 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.

   

Select the correct statement about paramagnetic substance

A uniformly charged rod with total charge '$Q$', length $l$ is initially at rest. In space uniform magnetic field '$B$' is present everywhere. Now an Impulse is imparted at centre of rod perpendicular to both, the magnetic field and the length of rod as shown in figure. So that it starts moving with uniform speed $v$. The mass distribution of rod is uniform. Total mass of rod is $m$. Ignore gravitational interactions.

Magnetic moment due to the motion of the electron in nth energy state of hydrogen atom is proportional to $n^x$ where$x$ is

A magnetic wire of dipole moment $4\mathrm{\pi } \mathrm{A} {\mathrm{m}}^2$ is bent in the form of semicircle. The new magnetic moment is

The magnetic dipole moment of current loop is independent of

A circular loop and a square loop are formed from two wires of same length and cross-section. Same current is passed through them. Then the ratio of their dipole moments is

A square loop is carrying a steady current $\mathrm{I}\mathrm{ }$ and the magnitude of its magnetic dipole moment is $\mathrm{m}$ . 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:

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

A circular coil of $300$ turns and diameter $14 \mathrm{cm}$ carries a current of $15 \mathrm{A}$. Magnitude of the magnetic dipole moment associated with the coil is 

Gyromagnetic ratio is the ratio of magnetic moment $\mu$ to the orbital angular momentum $\left(l\right)$. Its numerical value for an electron is given by.

What is gyromagnetic ratio?

Following figures shown the arrangement of bar magnets in different configurations. Each magnet has magnetic dipole moment $\overrightarrow{\mathrm{M}}$. Which configuration has minimum net magnetic dipole moment?

The magnetic dipole moment of a current loop is independent of

A circular coil of $300$ turns and diameter $14 \mathrm{cm}$ carries a current of $15 \mathrm{A}$. Magnitude of the magnetic dipole moment associated with the coil is 

Magnetic moment associated with the solenoid-

Two equal bar magnets are kept as shown in the figure. The direction if resultant magnetic field indicated by the arrow head at the point $\mathrm{P}$ is (approximately):-