Magnetic Materials & Magnets Test - 3

According to recent researches the magnetic field of earth is considered due to a large bar magnet situated in earth 's core.
It is considered that the north pole of this large magnet is situated at the geographical south of earth and vice versa and as the magnetic field due to a bar magnet is from north pole to south pole of the maget thus the earth 's magnetic field is considered from geographical south to geographical north which are respectively north and south poles of the bar magnet.

μ= μ₀ μ_r . μis the permeability of medium, μ₀ is permeability of free space, and μr is relative permeability of the medium.

B=B₀ +Bm
= μ₀ nI+ μmnI
=nI(μ+ μm)
=60x5(5000 μ₀ + μ₀ )
B=300(5001 μ₀ )
B=1.88T
H=B/μm
=300x5001 μ₀ /5000 μ
=300AT

Work required to turn the dipole is given by
W=MB[cos θ_i - cos θ_f ]
Here θi is the initial angle made by a dipole with a magnetic field and  is the final angle made by a dipole with a magnetic field.
magnetic moment is normal to the field direction.
so, θ_i =0 and θ_f =90
W = 1.5 ×0.22 [ cos0 °- cos90 °]
W = 0.33J
 
magnetic moment is opposite to the field direction.
so, θ_i =0 and θ_f =180
now, W = 1.5 ×0.22 [ cos0 °- cos180 °]
= 0.33 [ 1 - (-1) ]
= 0.66 J

The earth 's magnetic field is Be ​and its horizontal and vertical components are H_e ​and H_{v ​}
cos θ= H_{e ​​} /B_e ​
∴cos60^o = (​0.26 ×10^{−4 ​} / B_e )T
⇒B_e ​=(​0.26 ×10⁻⁴ )/ (½)​=0.52 ×10⁻⁴ T=0.52G

Explanation:As magnetic monopole does not exist. If we split the bar magnet into two pieces  each part will have its own north and south pole.

All substances show some kind of magnetic behaviour. After all, they are made up of charged particles: electrons and protons. It is the way in which electron clouds arrange themselves in atoms and how groups of these atoms behave that determines the magnetic properties of the material. The atom (or group of atoms) in effect becomes a magnetic dipole or a mini bar magnet that can align according to the magnetic field applied. The net effect of all these dipoles determines the magnetic properties of the Magnetic Materials.

Correct Answer :- C

Explanation : Magnetic Moment = Magnetization ×Volume

Side of cube = 20 cm

= 0.2 m

= 500 ×0.2 ×0.2 ×0.2

= 4Am²

 =1.5x0.22
 =15x22x10-3
 =330x10-3
Τ=0.33J
 

At null point (and along the axis), earth 's magnetic field and bar 's magnetic field are opposite in direction.
On the equatorial line, the bar 's magnetic field is opposite in direction to its field on the axis. Hence, on the equatorial line, the two fields add up.
As the null points are on the axis of the bar magnet, therefore,
B1= (μ0/4 π)(2M/d3)=H
On the equatorial line of magnet at same distance(d), field due to the magnet is  
B2= (μ0/4 π)(M/d3)=B1/2=H/2
Therefore, total magnetic field at this point on equatorial line is  
B=B2+H=3H/2=3 ×0.36G/2=0.54G