# Magnetism

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• Certain substances have a tendency to attract iron filings towards them, such substances are called magnetic substances and the property is known as magnetism.
• e.g. Iron, Steel, Cobalt, Nickel.
• The process of converting iron or its alloys into a magnet is called magnetisation.

#### Bar Magnet:

• A bar magnet is rectangular parallelopiped body which exhibits magnetic properties.
• When a bar magnet is suspended in air such that it is free to rotate about the transverse axis passing through its centre, then it is found that the bar magnet always aligns itself in the north-south direction.
• The end of the magnet which is pointing towards the geographical north is called north seeking pole or simply north pole, while the end of the magnet pointing towards the geographical south is called south seeking pole or simply south pole.
• Actually, the poles are not at the ends of the geometric length of the magnet but they are slightly inside.
• The length of the edge parallel to the magnetic axis is called geometric length of the bar magnet.
• The line joining the poles of the bar magnet to called an axis of the magnet.
• The distance between the poles of a bar magnet is called magnetic length.
• Magnetic length of bar magnet × 1.2 = Geometric length o the bar magnet.
• From the behaviour of a bar magnet, we can say that earth itself is behaving like a magnet. The magnetic north pole of the earth is at geographical south pole while the magnetic south pole of the earth is at geographical north pole.

#### Need of Analogy of Magnetic Circuit with Electric Circuit:

• If we try to break the bar magnet at the centre and separate the poles, new poles are formed at the broken ends.
• It means it is not possible for us to separate the poles and study them individually hence magnetic circuit is studied in analogy with the electrical circuit.
• Formulae & concepts are derived from an electrical circuit and by analogy formula for a magnetic circuit is written.

#### A Magnetic Monopole Does Not Exist:

• A bar magnet is said to have two poles located at the two ends of the magnet. If we try to break the bar magnet at the centre and separate the poles, new poles are formed at the broken ends. Thus two new magnets are formed each having two opposite poles at their ends.
• If the magnet is broken down into very small pieces further each piece will be a magnet with two poles. It means it is not possible for us to separate the poles. Thus we can say that a magnetic monopole does not exist.

#### Fictitious Poles:

• It is not possible to separate the two poles (the south pole and the north pole) by breaking the magnet into two parts. Similarly, it is not possible to locate the position of the poles of the magnet. Hence a magnetic dipole is supposed to be made up of two fictitious or imaginary poles.
• The position of these fictitious poles is found using compass needle. And it is found that they are not located exactly at the ends of the magnet but slightly inside.

Magnetic Length:

• A bar magnet is assumed to have two fictitious poles called the north pole and the south pole. The distance between the poles of a bar magnet is called the magnetic length of the magnet. It is denoted by ‘2l’.
• The length of the edge parallel to the magnetic axis is called geometric length of the bar magnet. Actually, the poles are not at the ends of the geometric length of the magnet but they are slightly inside.
• The relation between the magnetic length and the geometric length is
• Magnetic length of bar magnet × 1.2 = Geometric length of the bar magnet.

#### Magnetic Field:

• When a magnet is kept in a medium it sets around it what is called as a magnetic field.
• The magnetic field can be represented by drawing what is called as magnetic lines of forces. The direction of magnetic field at a point can be found by drawing a tangent to the line of force passing through that point.

#### Magnetic Lines of Force:

• A magnetic line of force is a curve drawn in the magnetic field in such a way that the tangent to the curve at any points gives the direction of magnetic field.

#### Characteristics of Magnetic Lines of Force:

• Magnetic lines of force are imaginary (hypothetical).
• Magnetic lines of force always emerges or start from north pole and always terminate on south pole.

• The lines of force emerged or terminate normally to the surface of the magnet.
• When two dissimilar poles of two magnets are brought near each other the lines of force assist each other hence there is an attraction between two poles.

• When two similar poles of two magnets are brought near each other the lines of force oppose each other and there is repulsion between the two poles.

• The lines of force never intersect each other if they do so it means that there are two direction for magnetic field at the point of intersection, which is not possible
• Lines of force have a tendency to shirk.
• Lines of force exert lateral pressure on each other.
• It is possible for us to draw magnetic lines of force through each and every point in the medium. But it will result in overcrowding of the lines. And then it will be impossible to study the magnetic lines of force individually and hence magnetic lines of force are group together into what is called as “tubes of forces”.
• If the tubes of force are crowded together then the magnetic field is strong.
• If the tubes are equally spaced then the magnetic field is uniform.
• If the medium is other than vacuum or air, tubes of force are called tubes of induction.

#### Magnetic Induction at a Point in Magnetic Field:

• The magnetic intensity or magnetic induction at any point in the magnetic field is equal to the number of tubes of force passing through the unit area of a small surface element drawn at that point.

B = ∅ / A

Where B = magnetic intensity or intensity of magnetic field or magnetic induction.

∅ = Magnetic flux.  Its unit as weber (Wb)

A = Area through which magnetic flux pass.

• Unit of Magnetic induction B is Wb/m² or tesla (T)

#### Magnetic Dipole:

• A magnetic dipole can be defined as two equal and opposite magnetic poles separated by a finite distance.
• Magnetic dipole consists of two equal and opposite magnetic charges having pole strength +m & -m separated by finite distance ‘2l’.

#### Magnetic Dipole Moment:

• The magnetic dipole moment is defined as the product of the pole strength and the magnetic length of a magnet.

M = m × 2l

• The magnetic dipole moment is a vector quantity. Its direction is from -m to + m i.e. from south pole to north pole.
• SI unit of Magnetic dipole moment is ampere. metre²  i.e. Am²

#### Force Acting on a Magnetic Pole Placed in Uniform Magnetic Field:

• If we try to break the bar magnet at the centre and separate the poles, new poles are formed at the broken ends. It means it is not possible for us to separate the poles and study them individually hence magnetic circuit is studied in analogy with the electrical circuit. Analogous to the quantity electrical field intensity we have similar quantity magnetic field intensity. It is also referred as the magnetic induction.
• The electrical field intensity at a point is defined as the force experienced by a unit charge kept at that point.

• By analogy, we can define magnetic induction at a point as the force experienced by a pole of unit strength kept at that point. Let the strength of the magnetic field be B.

• Thus the N-pole is acted upon by a force of magnitude mB and the south pole is acted upon by a force of magnitude mB, in the opposite direction to that on the north pole.

#### Torque Acting on a Magnet in a Uniform Magnetic Field:

• Let us consider a bar magnet of pole strength ‘m’ and magnetic length ‘2l’ suspended in a magnetic field of induction B such that it is free to rotate about a transverse axis passing through its centre. Let θ be the angle between the axis of the bar magnet and the direction of magnetic field.

The magnetic dipole moment of bar magnet is given by

M = m . 2l …………… (1)

Now, each pole of the bar magnet is acted upon by a force whose magnitude is given by

F = mB

• The force acting on north pole is equal to the force acting on the south pole but they act in opposite direction. Similarly, the lines of action of these two forces are different, Hence they form what is called a couple.

The magnitude of couple or moment of force is given by

Torque (t) = Force(F) . Perpendicular distance between the forces

∴ τ  =    F  . SP

∴ τ  =    F  . 2l sin θ          ……………….   (3)

From equations (2) and (3)

τ =    m B . 2l sin θ

∴ τ  =    (m . 2l ) . B  sin θ   ………………..(4)

From equations (1) and (4)

τ =    M B sin θ

This is an expression for the torque acting on a magnet kept in the magnetic field.

The direction of torque is perpendicular to the plane passing through .i.e. perpendicular to the plane of the paper.

#### Statement:

• If a bar magnet is free to rotate about an axis at right angles to two mutually perpendicular uniform magnetic fields of iinductions B1 and B2, then it comes to rest in a direction making an angle q with the direction of , such that

B2= B1 . tan q

#### Proof:

• It is found that when a bar magnet is suspended in two cross magnetic fields, it comes to rest with its axis along the direction of the resultant of the two magnetic fields.
• Consider a magnetic needle pivoted at the centre that it is capable of rotating about its vertical axis passing through its centre in the horizontal plane. It is found that the magnetic needle comes to rest along magnetic meridian under the action of the horizontal component of earth’s magnetic field of induction.

• Now, let the needle be subjected to another horizontal magnetic field of induction which is at right angles to BH. Under the action of these two magnetic fields the needle rotates through angle θ and come to rest along the resultant of these two magnetic fields.
• In the equilibrium condition, the needle is acted upon by two torques. one due to the magnetic field of induction given by mB.2l. cosθ and second due to the horizontal component of the earth given by mBH.2l. sin θ. Under the action of these two torques, the needle remains in equilibrium. Hence the two couples should be equal.

∴  mB . 2l . cos θ  = mBH . 2l. sin θ

∴   B . cos θ   = BH . sin θ

B = BH. sin θ / cos θ

B = BH. tan θ

This relation is called as tangent law.

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