Volume of the Cubic domain
\(V={ \left( { 10 }^{ -6 } \right) }^{ 3 }={ 10 }^{ -18 }{ m }^{ 3 }={ 10 }^{ -12 }{ cm }^{ 3 }\)
Mass of cubic domain
 \(m=V\times \rho ={ 10 }^{ -12 }\times 7.9\)
\(=7.9\times { 10 }^{ -12 }g\)
Number of atoms in the domain
 \(N=\frac { 7.9\times { 10 }^{ -12 }\times 6.023\times { 10 }^{ 23 } }{ 55 } =8.65\times { 10 }^{ 10 }atoms\)
Maximum possible dipole moment will be achieved when all the domains are completely aligned.
So \({ M }_{ max }=8.65\times { 10 }^{ 10 }\times 9.27\times { 10 }^{ -24 }=8.0\times { 10 }^{ -13 }{ Am }^{ 2 }\)
Magnetisation of the domain
 \({ m }_{ max }=\frac { { M }_{ max } }{ V } =\frac { 8.0\times { 10 }^{ -13 } }{ { 10 }^{ -18 } } =8.0\times { 10 }^{ 5 }{ Am }^{ -1 }\) 

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Parallel to and above the cable at a distance of 1.5 cm)

21600 div/amp.

Given, number of turns N = 120, current I = 3 A, radius of coil, r = 18 cm = 0.18 m and distance from the centre to a point on axis,
a = r = 0.18 m
As, \(\begin{aligned} B=\frac{\mu_0 N I a^2}{2\left(a^2+r^2\right)^{3 / 2}} \\ \end{aligned}\)
\(\begin{aligned} =\frac{4 \pi \times 10^{-7} \times 120 \times 3 \times(0.18)^2}{2\left[(0.18)^2+(0.18)^2\right]^{3 / 2}} \\ \end{aligned}\)
\(\begin{aligned} \Rightarrow \quad B & =4.4 \times 10^{-4} \mathrm{~T} \end{aligned}\)

Here, n = 2, I = 5.0 A,
B = 0.4 x 10^-3 T, r = ?
Magnetic field at the centre of current loop is
\(B=\frac { { \mu }_{ o } }{ 4\pi } \frac { 2\pi nI }{ r } \ or \ r=\frac { { \mu }_{ o } }{ 4\pi } \frac { 2\pi nI }{ B } \) 
\(\therefore \ r={ 10 }^{ -7 }\times 2\times \frac { 22 }{ 7 } \times \frac { 2\times 5.0 }{ 0.4\times { 10 }^{ -3 } } \) 
 = 157.1 x 10^-4m = 1.57 cm  

Consider two charges  \({ q }_{ 1 }\) and \({ q }_{ 2 }\) placed at a distance \(\left| { r }_{ 2 } \right| \) apart in air. The force between two charges
\(\left| \vec { { F }_{ e } } \right| =\frac { { q }_{ 1 }{ q }_{ 2 } }{ { 4\pi \varepsilon }_{ 0 } } \frac { 1 }{ { \left| { r }_{ 12 } \right| }^{ 2 } } \)  
Again consider two electrically neutral parallel current carrying elements of length  \({ dl }_{ 1 }\) and \({ dl }_{ 2 }\) carrying currents \({ I }_{ 1 }\) and \({ I }_{ 2 }\).
 \(\therefore \) Magnetic force between two current elements
\(\left| \vec { { F }_{ m } } \right| =\frac { { \mu }_{ 0 } }{ 4\pi } \frac { { I }_{ 1 }{ I }_{ 2 } }{ { \left| { r }_{ 12 } \right| }^{ 2 } } { dl }_{ 1 }{ dl }_{ 2 }\)
\( { I }_{ 1 }{ dl }_{ 1 }=\frac { { q }_{ 1 } }{ t } \times { dl }_{ 1 }={ q }_{ 1 }{ v }_{ 1 }\)
\({ I }_{ 2 }{ dl }_{ 2 }=\frac { { q }_{ 2 } }{ t } { dl }_{ 2 }={ q }_{ 2 }{ v }_{ 2 }\)
\( \left| \vec { { F }_{ m } } \right| =\frac { { \mu }_{ 0 } }{ 4\pi } \frac { { q }_{ 1 }{ q }_{ 2 } }{ { \left| { r }_{ 12 } \right| }^{ 2 } } { v }_{ 1 }{ v }_{ 2 }\quad ...(2)\)
\(\frac { \left| \vec { { F }_{ m } } \right| }{ \left| \vec { { F }_{ e } } \right| } ={ v }_{ 1 }{ v }_{ 2 }.{ \mu }_{ 0 }{ \varepsilon }_{ 1 }...(3)\)  
Since L.H.S. is a dimensionless quantity therefore, the quantity \({ \mu }_{ 0 }{ \varepsilon }_{ 1 }\) must have dimensions of \({ \left( velocity \right) }^{ 2 }\) as numerator has dimensions of \({ \left( velocity \right) }^{ 2 }\) as \({ v }_{ 1 }\) and \({ v }_{ 2 }\) are the drift velocities of electrons in current elements \(\therefore{ v }_{ 1 }{ v }_{ 2 }={ 10 }^{ -5 }\times { 10 }^{ -5 }\) 
\(={ 10 }^{ -10 }{ m }^{ 2 }{ s }^{ -2 }\) 
Where \({ \mu }_{ 0 }{ \varepsilon }_{ 1 }={ 1/c }^{ 2 }\), where c is velocity of light \(\left( { c }^{ 2 }=9\times { 10 }^{ 16 }{ m }^{ 2 }{ s }^{ -2 } \right) \) 
From (3)

\(\therefore \frac { \left| \vec { { F }_{ m } } \right| }{ \left| \vec { { F }_{ e } } \right| } <1\)

 \(\left| \vec { { F }_{ m } } \right| <\left| \vec { { F }_{ e } } \right| \)

On the basis of their in a magnetic field, the various materials can be classified in three classes.
(i) Diamagnetic: Those materials, which when placed in a magnetic field, are feebly magnetised in a direction opposite to the magnetising field are called diamagnetic substances.A few examples of diamagnetic materials are copper, zinc, bismuth, water, sodium chloride, helium, argon etc.
When a diamagnetic substance is suspended in a magnetic field, it arranges itself in the direction of the magnetic field.
(ii) Paramagnetic: Those materials, which when placed in a magnetic field, are feebly magnetised in the direction of magnetic field, are called paramagnetic substances.A few examples of paramagnetic substances are aluminium, sodium, antimony, platinum, copper chloride, liquid oxygen etc.
When a paramagnetic substance is suspended in a magnetic field it arranges itself to the direction of magnetic field.
(iii) Ferromagnetic: Those materials which when placed in a magnetic field are strongly magnetised in the direction of the magnetising field, are ferromagnetic substances.A few examples of ferromagnetic substances are iron, nickel, cobalt, alnico, mercury etc.

As we know for a charge particle moving in a magnetic fieldm the radius of circular Path r = mv/qB
As both the particles have same velocity therefore
r\(\alpha\)/rd = m\(\alpha\) qd/md q\(\alpha\) 
\(\frac { 4\times 1 }{ 2\times 2 } =\frac { 1 }{ 1 } \)

A parallel beam of electrons has electrons moving parallel to each other and a moving electron produces electric current and hence a magnetic field.
(i) When electrons are moving with the normal speed, then the electrostatic repulsion between electrons dominates the magnetic attraction between them. Due to it, the electron beam becomes diverging beam. 
(ii) When electrons are moving with high speed, then the magnetic attraction between them dominates the electrostatic repulsion between them. Due toit, the electron beam becomes converging beam.

\(=2\pi R\quad or\quad R=L/2\pi ;\)
Magnetic moment=\(IA=I\pi { R }^{ 2 }\)
\(=I\pi \left( \frac { L }{ 2\pi } \right) =I{ L }^{ 2 }/4\pi \) 

Magnetic dipole moment of a current loop = niA where n = no. of turns in a current loop; i = current through the loop and A = area of each turn of the loop. Magnetic dipole moment is a vector quantity. Its direction is perpendicular to the plane of loop directed outwards for anticlockwise current in loop and is directed inwards for clockwise current in loop.