Magnetism and Matter

Two identical small bar magnets each of dipole moment $3\sqrt5$ J/T are placed at a center to center separation of 10 cm, with their axes perpendicular to each other as shown in figure. The value of magnetic field at the point P midway between the magnets is $\alpha\times10^{-3}$ T. The value of $\alpha$ is ________.
($\mu_0=4\pi\times10^{-7}$ Tm/A)

The soft-iron is a suitable material for making an electromagnet. This is because soft-iron has

Given below are two statements :

Statement I : Susceptibilities of paramagnetic and ferromagnetic substances increase with decrease in temperature.

Statement II : Diamagnetism is a result of orbital motions of electrons developing magnetic moments opposite to the applied magnetic field.

Choose the correct answer from the options given below :-

A bar magnet having a magnetic moment of $2.0\times10^5$ J T$^{-1}$, is placed along the direction of uniform magnetic field of magnitude $B=14\times10^{-5}$ T. The work done in rotating the magnet slowly through 60° from the direction of field is :

A metallic conductor of length 1 m rotates in a vertical plane parallel to east-west direction about one of its end with angular velocity 5 rad s$^{-1}$. If the horizontal component of earth's magnetic field is $0.2\times10^{-4}$ T, then emf induced between the two ends of the conductor is :

The susceptibility of a paramagnetic material is 99. The permeability of the material in Wb/A-m, is :

[Permeability of free space $\mu_0=4\pi\times10^{-7}$ Wb/A-m]

A metallic rod of length 20 cm is placed in North-South direction and is moved at a constant speed of 20 m/s towards East. The horizontal component of the Earth's magnetic field at that place is $4\times10^{-3}$ T and the angle of dip is 45°. The emf induced in the rod is ______ mV.

The space inside a straight current carrying solenoid is filled with a magnetic material having magnetic susceptibility equal to $1.2\times10^{-5}$. What is fractional increase in the magnetic field inside solenoid with respect to air as medium inside the solenoid ?

At a certain place the angle of dip is 30° and the horizontal component of earth's magnetic field is 0.5 G. The earth's total magnetic field (in G), at that certain place, is :

The magnetic moment of an electron (e) revolving in an orbit around nucleus with an orbital angular momentum is given by :

Two bar magnets oscillate in a horizontal plane in earth's magnetic field with time periods of 3 s and 4 s respectively. If their moments of inertia are in the ratio of 3:2, then the ratio of their magnetic moments will be:

A magnet hung at 45° with magnetic meridian makes an angle of 60° with the horizontal. The actual value of the angle of dip is -

A compass needle of oscillation magnetometer oscillates 20 times per minute at a place P of dip 30°. The number of oscillations per minute become 10 at another place Q of 60° dip. The ratio of the total magnetic field at the two places $(B_Q:B_P)$ is :

The vertical component of the earth's magnetic field is $6\times10^{-5}$ T at any place where the angle of dip is 37°. The earth's resultant magnetic field at that place will be (Given tan 37° = $\frac34$)

A wire of length 8 m is bent to form a circular loop in y-z plane. A current of 0.5 A is flowing in anticlockwise direction in it, the magnetic dipole moment of the loop is:

A magnetic needle of magnetic moment $6.7\times10^{-2}$ Am$^2$ and moment of inertia $7.5\times10^{-6}$ kg m$^2$ is performing simple harmonic oscillations in a magnetic field of 0.01 T. Time taken for 10 complete oscillations is :

A magnetic dipole in a constant magnetic field has :

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

Hysteresis loops for two magnetic materials A and B are given below :

These materials are used to make magnets for electric generators, transformer core and electromagnet core. Then it is proper to use :

A magnetic dipole is acted upon by two magnetic fields which are inclined to each other at an angle of 75°. One of the fields has a magnitude of 15 mT. The dipole attains stable equilibrium at an angle of 30° with this field. The magnitude of the other field (in mT) is close to :