Magnetic Materials & Magnets Test - 4

A bar magnet may be thought of as a large number of circulating currents in analogy with a solenoid. On cutting a bar magnet in half we get two smaller solenoids with weaker magnetic properties.The field lines remain continuous, emerging from one face of the solenoid and entering into the other face. (i.e. similar magnetic fields). The magnetic moment of a bar magnet is also equal to the magnetic moment of an equivalent solenoid.
 

For paramagnetic materials orbital and spin magnetic moments of the electrons are of the order of bohr magneton.
Paramagnetic materials have some unpaired electrons due to these unpaired electrons the net magnetic moment of all electrons in an atom is not added up to zero. Hence atomic dipole exists in this case. On applying external magnetic field the atomic dipole aligns in the direction of the applied external magnetic field. In this way, paramagnetic materials are feebly magnetized in the direction of the magnetizing field.

If a magnet is suspended over a container of liquid air, it attracts droplets to its poles. The droplets contain only liquid oxygen; even though nitrogen is the primary constituent of air, it is not attracted to the magnet. Explain what this tells you about the magnetic susceptibilities of oxygen and nitrogen, and explain why a magnet in ordinary, room-temperature air doesn ’t attract molecules of oxygen gas to its poles.

Here M=0.48JT⁻¹ ,d=10cm=0.1m
On axis,
B= (μ_{0 ​​} /4 π)(2M/d3)​=10⁻⁷ ×(2 ×0.48/0.1³ )​=0.96 ×10⁻⁴ T

The needle will point along W-E if the result of the earth ’s magnetic field and magnetic field due to the coil have a resultant in the W-E direction. This happens if B cos 45^o =Earth 's field
⟹(μ0 ​nI ​/2r) cos45^o =(4 π×10 −7 ×30 ×0.35 ​)/(2 ×0.12) ×(1/√2)​​=0.39G=Earth 's magnetic field.

For a short Bar Magnet, the magnetic induction at a point on the axis at a distance r from centre is given by the formula
B= (μ0/4 π​​) (2M ​/r³ )
⇒B= K ​/ r³
⇒B ∝1/r³ ​
The correct answer is option D.

A ferromagnetic substance contains permanent atomic magnetic dipoles that are spontaneously oriented parallel to one another even in the absence of an external field. The magnetic repulsion between two dipoles aligned side by side with their moments in the same direction makes it difficult to understand the phenomenon of ferromagnetism. It is known that within a ferromagnetic material, there is a spontaneous alignment of atoms in large clusters. A new type of interaction, a quantum mechanical effect known as the exchange interaction, is involved. A highly simplified description of how the exchange interaction aligns electrons in ferromagnetic materials is given here.

Spin and Orbital angular momentum arise due to the presence of unpaired electrons. If there are unpaired electrons, these momenta will be there otherwise not.

Given,
Number of turns, N = 500 turns
Radius of solenoid, r = 2.9
Relative permeability of annealed iron of Km=1400
Permeability of free space,  μ₀ =4 π
The magnetic field, B=0.350 T
Therefore,
μ/μ₀ = μ_r
μ= μ_r x μ₀
B= μ_r μ₀ NI/2 πR
0.350=1400x4x 3.14x500xI/2x πx2.90
I=72.mA
 

The Bohr magneton μ_B ​is a physical constant and the natural unit for expressing the magnetic moment of an electron caused by either its orbital or spin angular momentum.
μ_{B ​} = e ℏ​/2me ​
where e is the elementary charge, ℏis the reduced Planck 's constant, me ​is the electron rest mass.
The value of Bohr magneton in SI units is 9.27400968(20)×10⁻²⁴ JT −1