•Introduction

•Bar Magnet

•Magnetism and Gauss`s law

•The earths magnetism

•Magnetisation and magnetic intensity

•Magnetic properties of material

•Permanent magnets and electromagnets

•Credit

Magnetic phenomenon are universal in nature. The word magnet is derived from the name of an island in Greece called

“MAGNESIA” where magnetic ore deposits were found. The directional properties of magnets are known since earlier times.

A thin long magnet when suspended freely pointed in the north south direction. The name LOADSTONE which is given to magnetite means leading stone.

The science of magnetism indeed blossomed with the publication of the famous book “DE MAGNETE” in 1600 written by WILLIAM GILLBERT.

* POSTULATES GIVEN BY WILLIAM GILBERT.

•The earth is a magnet with the magnetic field pointing from the geographic south to the north.It probably consist of a “giant bar magnet” placed approximately along its axis of rotation.

•When a bar magnet is freely suspended or floated in still water, it points in the north south direction. The tip towards geographic north is the north pole and that towards geographic south is south pole.

•There is a repulsive force when the two like poles are bought together and vice versa.

•We cannot isolate the north and the south pole.

•It is possible to make magnets out of iron and its alloys.BACK

• On examining iron fillings sprinkled on a sheet of glass over a short bar magnet,the pattern of iron fillings suggests that the magnet has 2 poles similar to the positive and negative charge of an electric dipole.

Related topics to bar magnet

•The magnetic field lines

•Bar magnet as an equivalent solenoid

•Dipole in a uniform magnetic field.

•Electrostatic analog

DEF: A uniform cubical piece of magnet is called a bar magnet. It resembles the shape of a bar

• The magnetic field lines are a visual and intuitive realization of the unseen magnetic field.

Their properties are as follows• The magnetic field lines of a magnet form

continuous closed loops.This is unlike the electric dipole where these lines begin on a positive charge and end on negative charge.

• The tangent to the field line at a given pt. represents the direction of the net magnetic field.

• Larger the no. of field lines crossing per unit normal area,larger is the magnitude of magnetic field.

The magnetic lines do not intersect. This is so since the direction of the magnetic field would not be unique at the point of intersection.

BACK

•The magnetic dipole moment m associated with a current loop is defined to be m = NiA where N is the no. of turns in a loop, I is the current and A is the area vector.

•The resemblance of magnetic field lines of a bar magnet and a solenoid suggests that a bar magnet may be thought of as a large no. of circulating currents in analogy with solenoid.

•Cutting a bar magnet into half is like cutting a solenoid into two smaller solenoids with weaker magnetic properties.

•TEST: Move a small compass needle in the neighborhood of a bar magnet and a current carrying solenoid. Deflections of the needle will be similar in both the cases.

Similarities in Axial fields of bar magnet and a solenoid.

Let the above solenoid consist of n turns per unit length of radius a. Let its length be 2l. We can evaluate the axial field at a distance r from the center of the solenoid to do this consider a circular element dx of the solenoid at a distance x from the center. It consists of ndx terms. Let I be the current in the solenoid. The magnitude of the field at a pt. P due to circular element is dB= μondxia2

2{(r-x)2+a2}3/2

The magnitude of the total field is given by integrating x from –l to +l which comes out to be

~ μoni 2la2

2 r3

Magnitude of the magnetic moment of the solenoid is

M = n (2l) I(⊼ a2)

( Total no. of turns *current*cross sectional area)

Thus

B ~ μo 2m

4⊼ r3 BACK

The pattern of iron filing and the magnetic field lines give us an approximate idea of the magnetic moment m and its field B.

Thus, the torque on the needle is

τ = m * B

τ(θ) = mBsinθ

From Newton`s second law

I d2 θ ~ -mBθ

dt2

This represents simple harmonic motion. The sq of angular frequency w2 = mB/I. The time period is

T = 2 (l/mB)⊼ 1/2

BACK

Magnetic field at large distances due to a bar magnet of magnetic moment m can be obtained from the equation for electric field due to an electric dipole of dipole moments by making the following replacements:

E → B

p → m

1 → μo

4Eo 4 ⊼ ⊼

In particular we can write down the equatorial field(BE) of a bar magnet at a distance r for r>>l , where l is the size of the magnet.

BE = -μom /4 ⊼ r3

Likewise, the axial field (BA) of a bar magnet for r>>l is

BA= 2μom /4 ⊼ r3

BACK

GAUSS LAW is applicable in Electrostatics but in Magnetism it’s application is different as in case of magnetism the magnetic field of lines forms closed loops .

Consider a small vector area element Δ S of a closed surface S . The magnetic flux through Δ S is defined as

Δ ØB = B. Δ S

Where, B is the field at Δ S .

We divide S into many small area elements & calculate flux through each. Then the net flux ØB is

ØB = Σ Δ ØB = Σ B. Δ S

Thus GAUSS LAW for magnetism is :

“ The net magnetic flux through any closed surface is zero.”

Gauss law is the reflection of the fact that isolated magnetic poles do not exist. There is no source or sink of B.

The value of gravitational field on the earth surface is few tenths of Gauss (1 G = 10-4T). This magnetic field was thought of arising of a gigantic bar magnet placed approximately along the axis of rotation of the earth and deep in its interior.

Let us denote the geographical north and south poles by Ng

and Sg respectively. The magnetic axis of the earth makes an angle of approx. 20 degree with the geographic axis. Since the north pole of the compass needle pts. Approx. to the geographic north Ng, we designate the earths magnetic pole close to Ng as Sm ,the south magnetic pole. Similarly Nm the north magnetic pole of the earth is close to Sg.

Sm is located at a pt. In northern canada with latitude at 70.5 degree north and longitude at 96 degree west. Nm is located at a pt. Diametrically opposite 70.5 degree south and 84 degree east.

RELATED TOPICS TO EARTH`S MAGNETISM

•Magnetic declination and dip.

•Origin of the earth`s magnetic field

•Global variation in the earth`s magnetic field.

•Temporal variation in the earth`s magnetic field.

Consider a pt P on earths surface say Delhi. At this pt.,the longitude determines the north south direction. The vertical plane containing the vertical axis is called the geographic meridian. At P there also exists the earths magnetic field B.The magnetic meridian is the vertical plane containing B and the vertical axis.

The angle between the geographic and the magnetic meridian planes is called the magnetic declination.

As we move north from the equator, the magnetic field changes direction and dips down. The angle that magnetic meridian makes with the horizontal is called the dip angle. The dip angle is determined by using a dip circle or a dip meter.

BACK

The magnetic field of the earth can be approxim,ated by a gtiant bar magnet located deep inside the earth. The earth does have large deposits of iron ore deep inside but it is highly unlikely that any large solid mass of magnetic material is responsible for earths magnetism.

The earths core is very hot and molten circulating ions. In the highly conducting liquid region of the earths core could form current loops and produce a magnetic field.

That is why moon do not have any magnetic field as it does not possess any molten core.Venus which has slower rate of rotation has a weaker magnetic field. On the other hand, Jupiter has a faster rotation rate and hence a stronger magnetic field.

•But no one knows what is the precise mode of action and the energy needed to sustain such circulating currents!!

BACK

The dipole approximation suggests that the earths magnetic field falls below a micro tesla at a distance of five times the earths radius i.e. at about 30 thousand km.

Beyond this the solar wind disturbs the dipole pattern. The solar wind consist of screen of charged particles that emerges continuously from the sum. The charged particles of the solar wind get trapped near the magnetic pole of the earth. They ionize the atmosphere above these poles which in turn causes a spectacular display of light in the shape of giant curtains high up in the atmosphere./

In the arctic region it is called the “aurora borealis” or northern lights and in the south it is called “aurora australis”.

BACK

The earths magnetic field is found to change with time. These changes can be characterized into short term and long term. In short term,magnetic poles of earth S and N keep shifting their positions.

Changes in the earth’s magnetic field over long term or geological time scales are quite interesting. It appears that earths field has reversed itself every million year or so. The evidence of the same come from basalt which contain iron and it is emitted during volcanic activity on ocean floor. opposite direction.

As basalt cools, it solidifies and provides a picture earths magnetic field and direction. The basalt can be dated by other means and thus clear picture of reversal of earths magnetic field over reversal time scales has emerged. These reversal means that one in million years or so, the current in the earths core slow down, come to halt, and then pick up the

BACK

The Earth abounds with a bewildering variety of elments and compounds. In addition we have been synthesising new alloys, compounds and even elements.

Consider a solenoid of n turns per unit length and carrying a current I. The magnetic field in the interior of the solenoid is,

B0 = µ0 n I

The magnetic intensity H is a quantity related to current in coils 7 conductors. In this case it is defined as

H = B0 / µ0

H = n I

The magnetic intensity is a vector with dimension of L-1 A. Its S.I unit is A m-1 ( Ampere / metre).

We will next fill the solenoid with a magnetic material keeping the current I constant. The total field B inside will be different from B0. The additional field will be due to magnetic material under the influence of B0. Let this magnetic material posses a dipole moment m.

We define the relevant quantity called Magnetisation M which is equal to the magnetic moment per unit volume(V).

M = m / V

M is a vector with dimension L –1 A and unit A m –1.

Thus additional magnetic field inside is µ0 M & the total field is

B = B0 + µ0 M

= µ0 ( H + M)

The magnetic field due to specific nature of the magnetic material M can be influenced by external factors which is expressed

M = χ H

Where χ , a dimensionless quantity is approximately called the Magnetic Susceptibility. It is a measure of how a magnetic material respond to an external field.

• χ is small & positive for materials which are called Paramagnets.

χ is small & negative for materials which are called Diamagnets.

Thus

B = µ0 (1+ χ) H

= µ0 µr H

= µ H

Here µr = 1 + χ is a dimensionless quantity called the relative magnetic permeability of the substance.

The magnetic permeability of the substance is µ & it has the same units as µ0.

Materials are classified on the basis of susceptibility χ as

• Diamagnetic if χ is negative

• Paramagnetic if χ is positive & small

• Ferromagnetic if χ is positive & large

Detailed Information regarding different types of material :

• DIAMAGNETISM

• PARAMAGNETISM

• FERROMAGNETISM

The individual atoms,or ions or molecules do not possess a permanent dipole moment of their own. The application of an external magnetic field B induces in each atom, a small dipole moment proportional to B but in opposite direction. The field lines are expelled or repelled and field intensity is reduced.

When placed in a uniform magnetic field, the bar will tern d to move from high to low.

Some diamagnetic materials are bisumith, copper lead, nitrogen at STP etc.

The most exotic diamagnetic materials are Type-I super conductors. These are metals cooled to very low temperatures which exhibit both perfect conductivity and perfect diamagnetism.

The phenomenon of perfect diamagnetism is called MEISSNER EFFECT.It can be gain fully exploited in variety of situations. E.g. for running magnetic leviated super fast trains.

BACK

The individual atom of paramagnetic material posess the permanent dipole moment of its own.

On the account of ceaseless random motion of the atoms, no net magnetization is seen. In the presence of external field B which is strong enough ,and at low temperatures, the individual atomic dipole moments can be made to align and point ion the sanme direction as B. The field line gets concentrated inside the material and field intensity is enhanced inside. When placed in non uniform magnetic field, bar will move from low to high.

Some paramagnetic materials are aluminum,sodium calcium,oxygen at STP and copper chloride.

M = C B0 / T

Or equivalent to

χ =Cμo / T

The constant C is called curies constant.Thus, for a paramagnetic material, both χ and μr. Depends not only on the material but also on the sample temperature. At very high fields or at very low temp., the magnetization approaches its max. value when all atomic dipole moments are aligned. This is called the saturation magnetization value. Ms… Beyond this, curies law is no longer valid.

Experimentally one finds that the magnetisation of paramagnetic material is directly proportional to the absolute temperature T.

BACK

The individual atoms in a ferromagnetic material possess a dipole moment.

However, they interact with one another in such a way that they spontaneously align themselves in a common direction over a microscopic volume called domain.

Each domain has a net magnetization. Typical domain sizes 1 mm and the domain contain about 100,000,000,000 atoms.

In the first instance, the magnetization varies randomly from domain to domain and there is no bulk magnetization.

When we apply an external magnetic field B0,the domain orient themselves in the direction of B0. And simultaneously they grow in size.

In a ferromagnetic material, the magnetic field lines are highly concentrated.

In some Ferro magnets, magnetic materials even after removing the external field, the magnetization persists. Such materials are called “Hard magnetic materials or hard Ferro magnets” .

ALNICO an alloy of aluminum, iron ,nickel ,cobalt and copper is one such material.

There is a class of ferromagnetic materials in which the magnetization disappears on removal of the external field. Soft iron is one such material. Such materials are called soft ferromagnetic materials.

The ferromagnetic property depends upon temperature.At high enough temperatures, a ferromagnet becomes a paramagnet. The domain structure disintegrates with temperature.

BACK

Substances which at room Temperature retain their magnetic properties for a long period of time are called Permanent Magnets.

There are no. of ways of making permanent magnets :

• One can hold an iron rod in the north & south direction and hammer it repeatedly.

• One can hold a steel rod and stroke it with one end of the bar magnet a large no. of times , always in the same sense to make permanent magnets.

•An efficient way to make permanent magnet is to place a ferromagnetic rod in a solenoid & pass the current. The magnetic field magnetises the rod .

Characteristics of the material for making Permanent Magnets :

• The material should have high retentivity so that the magnet is strong .

• The material should have high coercivity so that the magnetisation is not erased by stray magnetic field , temperature fluctuations & minor mechanical damage .

• Further the material should have a high permeability.

• Suitable material material for making permanent magnets are : Steel , Alnico , Cobalt steel & Ticonal .

ELECTROMAGNETS are made of ferromagnetic material which have high permeability & low retentivity .

Soft Iron is a suitable material for electromagnets .

On placing the soft iron in a solenoid by a thousands of fold. When we switch off the solenoid curent , the magnetism is effectively switched off since the soft iron core has low retentivity.

In certain cases , the material goes through an ac cycle of magnetisation for a long period .This is a case in Transformers & Telephone diaphragms .

Electromagnets are used in electric bells , loudspeakers and telephone diaphragms. Giant electromagnets are used in cranes .

The temperature of transition from ferromagnetism to para magnetism is called curie temperature Tc.

The susceptibility above the curie temperature, I.e. in the para magnetic phase is described by

χ = C / (T- Tc.) {T > Tc} where C is constant.

Our sincere thanks to:

Our Physics Teacher Mrs. Yashu Kumar

Source : Physics NCERT textbook for class XII

Project Prepared by :

Nitish Goel of class XII - D

Varun Dutt of class XII - D