Download Notes on Magnetism

Notes on Magnetism
1.
A magnet is any substance that attracts iron. ( That a mgnet attracts other
substances is true but that it attracts iron is sufficient to call it a magnet ).
2.
The following observations were made about magnets
3.
(i)
The attraction is maximum at two points in the magnets. (These
points are named as poles of the magnets and the line segment
joining these points is named as the axis of the magnet.
(ii)
When a magnet is suspended freely with the magnetic axis parallel
to the groung, one particular pole always tries to point out in the
north direction. This pole is named as the north seeking pole of the
magnet or simply north pole of the magnet. Obviously, we have no
choice but to call the other pole as south pole.
(iii)
Likes pole repel and unlike poles attract
(iv)
There are no magnets with single pole. If a magnet is broken into
two pieces , each piece automatically acquires two ples.
(v)
The force of attraction or repulsion between two poles is found to
be inversely proportional to the sqyuare of the distance between
them (Weber?).
(vi)
The force with which a north pole is repelled by a north pole of a
magnet is same as the force with which the south pole of the same
magnet is attracted by the given north pole. So, we may have both
the poles of the magnet have same strength for attraction and
repulsion.
Now, the question is, is it possible to define the above mentioned strength
of the magnet ? Remember, measuring means comparing. To do this we
must first make a postulate that every pole of a magnet has what may be
called pole strength which is indicative of its ability to attract or repel
other poles. First, we need to define the equality of pole strengths. This is
quite easy. Two pole strengths are said to be equal if both of them attract
or repel a given pole from a given distance with the same strength.
Suppose A,B,C are three poles. Suppose A attracts C with twice the force
as B attracts C. Now, I may define the pole strength of A to be twice that
of B. In so defining, the force between two poles becomes proportional to
the product of the pole strengths. The above definition is not a random
one but in tune with the observations. What remained is to define the unit
of the pole strength.
4.
For a moment let us call m and n as the pole strengths of two poles
separated by a distance d and the force between them is found to be F. So
far, we found that 𝐹 ∝ 𝑚𝑛/𝑑 2 . i.e., = 𝑘𝑚𝑛/𝑑 2 . If we assume that the
force between poles of magnet depends on pole strength and their
separation alone, it would be convenient to define unit of pole strength in
such a way that k becomes 1. ( We did likewise in defining unit of force).
We may define a unit of pole strength as “ two poles of equal strengths
are said to be having a pole strength of one unit if they exert a force of 1
Newton when separated by 1 meter”. This unit may be called one Tom.
5.
A magnetic field is said to exist in a region or space if a magnet
experiences a force (obviously magnetic force) at that region.Just like it
became important for us to measure pole strength, it is very much
important for us to measure magnetic field because at different points the
magnetic forces are different.The question how much is the field is more
important than whether field exists or not. We quantify the magnetic field
as follows: To every point in the magnetic field, we associate some
strength and direction i.e., with every point in the magnetic field we
associate a vector. The magnitude of the field at pont may be defined as
the force experienced by a pole of unit pole strength. The direction of the
field , by convention, shall be taken as the direction of motion of north
pole at that point.This vector is usually represented as → and is called the
𝐵
Magnetic Field Vector at the point. ( For historical reasons, this vector
has so many names). Obviously, the unit of → is Newton per Tom.
𝐵
6.
A magnetic line of force, by definition, is the path traced by a north pole.
By this definition, the following things are implied
(i)
A MLF starts from north pole and ends in south pole.
(ii)
No two MLFs intersect
(iii)
The magnetic field vector at any point on a MLF is
tangential to that point.
Why do we need MLFs at all?
7.
Actually, at any point in region or space, where there a magnetic field,
there is an MLF. But if we draw all these MLFs, we do not get lines at all,
let alone the lines “representing” the field. So, magnetic lines are drawn
in such a way to indicate the strength, direction and variation of magnetic
field. Lines of force drawn such that the number of lines passing norm,al
to an area per unit area gives the magnitude of field strength at that point.
The number of lines passing through an area is called that magnetic flux
through the area. The magnetic flux per unit area is called flux density.
So, by definition, numerically, magnetic field strength is same as flux
density.
8.
In 1600, Gilbert realised that earth itself is a magnet.
9.
The year 1819 changed the whole story of Magnetism. While Oersted
discovered that a moving charge produces a magnetic field, Ampere,
later, realised that moving charge alone produces a magnetic field. In a
way, magnetic field became more fundamental than magnet.Various
questions arised which can be put into two categories
(i)
Magnetic effects of moving charges
(ii)
Behaviour of a moving charge in a magnetic field.
While Lorentz quantified the second aspect, Biot & Savart quantified the
first aspect.
Because magnetic field assumed significance over magnet, the unit of
magnetic field is first defined and the pole strength is then defined in
terms of unit of magnetic field strength.
10.
It is observed that a charged particle at rest do not experience any force.
But if a charged particle with is moving with a velocity → in a magnetic
𝑣
field → then a force is experienced by that particle which is perpendicular
𝐵
to the plane containing vectors representing → and → (By observation).
𝑣
𝐵
It is also found that the force acting on the particle is proportional to the
charge of the particle, speed of the particle and magnetic field strength.
So, the force on the particle is given as 𝑘𝑞(→ × → ), where k is a constant
𝑣
𝐵
of proportionality. Now, the unit of magnetic field is defined in such a
way that k becomes 1. “ A magnetic field which produces a force of one
newton on a charge of one coulomb moving at a speed of one metre per
seond is defined to be magnetic field of one unit.”This unit of magnetic
field is called Tesla. We can observe that Tesla is Newton per Amp.Met.
Because magnetic field is defined as force per unit pole strength, pole
strength is the magnetic force per unit magnetic field.So, the unit of pole
strength is necessarily N/T viz. N/(N/A.m) viz. A.m.It now remains to
relate unit of pole strength i.e., A.m with 1 Tom. Rather that relating A.m
and Tom we change k in point 4. It was observed that the value of k
actually depends on the material that separates the poles. If no material is
present ( if vaccum is present) , k is found to be 10−7 𝑁/𝐴2 and this value
is given a special name ( absolute permeability) and a special symbol
(𝜇𝑜 ).