MAGNETISM, MAGNETIC FIELD DUE TO A BAR MAGNET

MAGNETISM

1. Magnetic substances:-
The substances that are attracted by a magnet are called magnetic substances.
Magnetic substances can be made into magnets.
Examples:-
Iron(Fe),Cobalt(Co), Nickel(Ni), etc.,.

2. Non-Magnetic substances:-
The substances that are not attracted by a magnet are called ‘Non-Magnetic substances’.
Non-Magnetic substances cannot be made into magnets.
Examples:-
Plastic, wood, brass, paper, etc.,.

3. Differences between magnetic and non-magnetic substances

Magnetic substances Non-Magnetic substances
1.  The substances that are attracted by a magnet are called ‘magnetic substances’. 1.  The substances that are  not attracted by a magnets are called ‘ non-magnetic substances’.
2.  Magnetic substances can be made into magnets. 2. Non- Magnetic substances can  not be made into magnets.
3.  Examples are iron, cobalt, nickel etc.,. Examples are Plastic, wood, brass, paper, etc.,.

4. Assumptions of Ewing’s Molecular Theory
1. Every molecule of a magnetic substance acts as a tiny magnet.

2. In an unmagnetised substance, the molecular magnets are not arranged in any order.

3. In a magnetized substance the molecules are arranged in an order. In this order the north poles of all the molecules of the magnetized substance are directed towards one end and their south poles are directed towards the opposite end.

4. Inside the magnetised iron-bar the north pole of each elementary magnet is coupled to the south pole of next magnet and so on. However, there are free North poles at one end and free south poles at the other end. These free poles make the iron-bar as a whole magnet with two poles(North, South). These two poles are the ‘points’ where N and S poles of the molecular magnets are left free or uncoupled.

5. Repetition of the process of magnetization increases the alignment of molecular magnets and reaches a maximum limit called ‘Magnetic saturation’ where further magnetization is not possible.

6. When the magnetized iron-bar is cut into number of smaller and smaller pieces, each piece acts as an individual magnet with north and south poles.

7. Magnetic poles always exist in pairs.

8. Magnetism of a magnet can be destroyed by tapping, hammering, heating etc.,.

5. Failures of Ewing’s Molecular Theory:-
Ewing’s molecular theory failed to explain why
1. the individual molecules of a magnetic substance like iron behave as tiny magnets;

2. the individual molecules of a non-magnetic substances like brass or saw-dust are not magnets;

3. the substances like bismuth or copper are repelled by a strong magnet.

6. Why isolated magnetic poles do not exist
If we cut a bar-magnet into smaller and smaller pieces, every piece behaves as a magnet. It has its own north and south poles. So, isolated magnetic poles do not exist.

INVERSE SQUARE LAW OF MAGNETISM

1. Pole strength of a bar-magnet:-
The ability of a pole of a magnet to attract or repel another magnetic pole is called its ‘pole strength’.

2. Inverse Square Law of Magnetism:-
The inverse square law of magnetism states that the force of attraction or repulsion between the two magnetic poles is directly proportional to the product of their pole strengths and inversely proportional to the square of the distance between them and acts along the line joining the poles.

3. Relation ship between the Magnetic force (F) and magnetic pole strength m1 and m2 and distance between the magnetic pole ‘r’
or
Derivation of .
Let,
m1 and m2 be the pole strengths of two magnetic poles separated by a distance ‘r’.
According to the inverse square law of magnetism.

1. The force between two magnetic poles is directly proportional to the product of their pole strengths.

2. The force between two magnetic poles is inversely proportional to the square of distance between them.

From equations (1) and (2) we have,


Where,
‘k’ is called the constant of proportionality.

Note:-
1. In S.I. system the value of K is equal to .

Where,
μ0=Magnetic permeability of free space or air.

2. If the medium is other than free space or air then

Where,
μ=Absolute magnetic permeability of the medium .

4. Magnetic Permeability(μ):-
Magnetic permeability of a medium is defined as the ability to allow the magnetic lines of force to pass through it (or) to allow itself to be influenced by the magnetic field.
Unit of permeability:-
Unit of permeability is Henry/metre.

5. Relative permeability:-
The ratio of the magnetic force in a medium to magnetic force in free space is defined as relative permeability of the medium.
Relative permeability
μ= μr.μ0

Note:-
1. The M.K.S. unit of pole strength is ‘Weber’.
2. S.I. unit of pole strength is Am.(Ampere. meter)
3. 1. Weber= μ0Am.
4. relative permeability
μ= μr.μ0

5. Value of μ0=4Пx10-7 Henry/meter.

6. How is relative permeability related with absolute permeability of a medium
Or
Derive (or) μ=μrμ0.
1. In S.I. system, the form of inverse square law in free space is given by

2. Instead of free-space, if any other medium exists, the inverse square law in eq(1) takes the form

3. Dividing eq(2) by eq(1) we get,

4. This ratio of the magnetic force in a medium to the magnetic force in free space is defined as “relative permeability, μr”.


(or)
μ=μrμ0
where,
μ=Absolute magnetic permeability of the medium.

7. Unit Magnetic Pole (or) Unit pole Strength:-
The unit magnetic pole (or) unit pole strength is defined as that pole which repels an identical pole at 1 meter distance with a force of 10-7N.

8. Magnetic flux:-(Φ)
The total number of magnetic lines of force in a given area is called ‘magnetic flux’.

9. Magnetic field induction (or) Magnetic Flux Density:- (B)
Magnetic field induction or magnetic flux density is defined as the magnetic flux passing through a unit normal area;

10. Magnetic field induction:-
The Magnetic induction B due to a magnet at a point in a medium is defined as the force acting on a unit north pole placed at the point.

Note:-
1.

 

 

 

Where,
m=pole strength.
B=magnetic field induction.
F=force.

5. Unit of magnetic field induction (B) is Weber/metre2 (OR) Newton/Am (OR) Tesla.

6. 1 Tesla = 104 Gauss (or) 1 Weber/m2.

7. C.G.S. unit of B is Gauss.

11. Intensity of Magnetic Field (H):-
The intensity of magnetic field H at a point is defined as the force acting on a unit north pole placed at the point, independent of the medium.
Note:-
1. In C.G.S. system H= .

2. In M.K.S. system H=

3. S.I. unit of H=ampere/meter(A/m).

4. B=μ0H.

12. Difference between absolute and relative permeability

Absolute permeability Relative permeability
1.  Absolute permeability is the ability of the free-space to allow the magnetic lines of force to pass through it or to allow itself to be influenced by the magnetic field. 1.  Relative permeability is  the ratio of the magnetic force in a medium to the magnetic force in free space.
2.  It is denoted by μ0 and its value =4Пx10-7 Henry/metre. 2.  It is denoted by the symbol μr.

 MAGNETIC FIELD DUE TO A BAR MAGNET

1. Magnetic moment:-
Magnetic moment(M) of a bar-magnet is defined as the product of its pole strength (m) and magnetic length (2l).
M = mx2l.

Note:-
The S.I unit of magnetic moment is Am2.(ampere-metre2).

2. Axial line:-
An imaginary line joining the north and south poles and passing through the centre of mass of a magnet is called the axial line.

3. Magnetic field induction on the axial line:-
The magnetic field induction on the axial line is given by

Where,
μ0=Absolute magnetic permeability of free space.
M=magnetic moment.
d=distance of a point from the centre of the mass of the magnet.

4. Equatorial line:-
An imaginary line passing through the centre of the mass of the magnet and perpendicular to the line joining the poles of the bar magnet is called Equatorial line.

5. Magnetic field induction on the Equatorial line:-
The magnetic field induction on equatorial line is given by

Where,
μ0=Absolute magnetic permeability of free space.
M=magnetic moment.
d=distance of a point from the centre of the mass of the magnet.

6. How do you measure the magnetic moment
Magnetic moment of a bar-magnet is measured by the product of its pole strength (m) and its magnetic length (2l).
M=21.m

MAPPING OF MAGNETIC LINES OF FORCE DUE TO A BAR MAGNET NEUTRAL POINTS

1. Neutral point or Null point:-
A point where the magnetic field induction(B) due to a bar-magnet is equal in magnitude and opposite in direction to the horizontal component of the earth’s magnetic field induction (B0) is called a neutral point.
Or
A point at which the magnetic field induction (B0) due to a bar magnet is nullified by the horizontal component of earth’s magnetic field induction is called a neutral point for the bar-magnet.

2. How do you locate the neutral points when the north pole of the magnet faces the geographical north of the earth

1. Fix a drawing sheet on a drawing board.

2. Take a compass needle and identify the magnetic meridian.

3. Draw a line with an arrow at a corner of the paper to indicate the same as shown in the figure.

4. This line indicates the direction of the horizontal component of the earth’s magnetic field induction.

5. Place the bar magnet at the centre of the paper on the magnetic meridian with its north pole pointing the north pole of the earth. Draw its outline.

6. Now, draw the magnetic lines of force with the help of a compass needle on both the sides of a magnet.

7. The magnetic lines of force will be as shown in the figure.

8. The null points (neutral points) N1 and N2 are obtained on either sides of the bar-magnet at equal distance from it.

9. At these null points the magnetic field induction due to a bar-magnet is equal in magnitude and opposite in direction to the horizontal component of the earth’s magnetic field induction. Hence, the resultant magnetic field becomes zero.

10. These null points or neutral points are located on the equatorial line.

3. Describe an experiment to locate the neutral points when the south pole of the bar magnet points towards the geographical north pole of the earth

1. Fix a drawing sheet on a drawing board.

2. Take a compass needle and identify the magnetic meridian.

3. Draw a line with an arrow at a corner of the paper to indicate the same as shown in the figure.

4. This line indicates the direction of the horizontal component of the earth’s magnetic field induction.

5. Place the bar magnet at the center of the paper on the magnetic meridian with its south pole pointing the north pole of the earth. Draw its outline.

6. Now, draw the magnetic lines of force with the help of a compass needle on both the sides of a magnet.

7. The magnetic lines of force will be as shown in the figure.

8. The null points are formed at the points N1 and N2 i.e., one at the top of the south pole and the other below the north pole of the magnet at equal distance from the center of the magnet.

9. At these null points the magnetic field induction due to a bar-magnet is equal in magnitude and opposite in direction to the horizontal component of the earth’s magnetic field induction. Hence, the resultant magnetic field becomes zero.

10. These null points lie on the axial line of the bar-magnet.

4. How do you calculate the magnetic moment and pole strength of a bar magnet from the knowledge of null points of bar magnets
1. If we have the knowledge of B0 at a place, we can calculate magnetic moment(M) and pole strength(m) of the bar magnet. For example, the B0 value in Andhra Pradesh is 0.39×10-4 Tesla.
Case(i):-
When the neutral points are on the equatorial line of a bar magnet at a distance ‘d’ from the center of the magnet, the magnetic field induction (B) is given by

Case2:-
When the neutral points are on the axial line at a distance ‘d’ from its centre, the magnetic field induction is given by

 

 

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