Comprehensive Guide to Magnetic Materials and Earth's Magnetism

based on magnetic susceptibility and relative magnetic permeability of materials

they are classified into three categories namely

magnetic paramagnetic and ferromagnetic materials now let us discuss the properties of

these materials starting off with the diamagnetic materials diamagnetic materials are the materials

that are repelled by magnets when a part of diamagnetic material is placed in a non-uniform external

magnetic field it tends to move from a region of strong magnetic field to a weaker magnetic

field we also observe that the magnetic field lines are expelled or repelled by the

diamagnetic material and the magnetic field inside the material is reduced let us discuss the causes of

diamagnetism we know that the orbiting electrons around the nucleus in an atom are

equivalent to the current carrying loops these electrons possess an orbital magnetic moment

for a diamagnetic material the resultant magnetic moment of all the electrons in an atom is zero

when the diamagnetic material is placed in an external magnetic field due to induced current

the movement of the electrons for which the orbital magnetic moment is in the same direction as that of the external

magnetic field is slowed down and the orbital magnetic moment of the electron decreases

likewise the movement of the electrons for which the orbital magnetic moment is in the

opposite direction to that of the external magnetic field is sped up and the orbital magnetic moment of the

electron increases the material then develops a resultant magnetic field in the direction opposite

to that of the external magnetic field hence the diamagnetic materials are repelled by the external magnetic field

although time magnetism is present in all materials its effect is very weak in most of them

some examples of diamagnetic substances are bismuth copper lead silicon and nitrogen at STP

magnetic susceptibility of the diamagnetic substances is greater than or equal to minus one and less than zero

relative magnetic permeability of these substances is greater than or equal to zero and less than one

superconductors exhibit perfect diamagnets ISM when a material is cooled below its

transition temperature it becomes a superconductor in superconducting state the material

behaves as a perfect conductor of electricity and a perfect diamagnetic material

when a material makes a transition from the normal state to the superconducting state

it actively excludes the magnetic field from its interior and hence repeal magnets

this is called Messner effect maglev trains or another words magnetically levitated superfast trains

work on the same principle let us discuss about paramagnetic materials

paramagnetic materials are the materials that are weakly attracted by the magnets when about of paramagnetic material is

placed in a non-uniform external magnetic field it tends to move from a region of weak magnetic field to a

stronger magnetic field the magnetic field lines get concentrated in the paramagnetic

material and the magnetic field inside the material increases

now let us discuss about the causes of paramagnetism in case of paramagnetic material

individual atoms possess a permanent magnetic dipole moment due to the orbiting electrons in the atom

but due to random thermal motion of the atoms the net magnetic moment of the material

is zero when a paramagnetic material is placed in an external magnetic field of

induction be not at low temperatures the magnetic dipole moment of the individual atoms aligned in the same

direction as of the external magnetic field some examples of paramagnetic materials

are aluminium sodium calcium etc magnetic susceptibility of paramagnetic materials is small and positive

relative magnetic permeability of these materials is slightly greater than one a paramagnetic material placed in an

external magnetic field gets weakly magnetized the magnetization of the paramagnetic

material is inversely proportional to its absolute temperature that is

I is inversely proportional to T let this be equation 1 the magnetization is directly

proportional to the applied magnetic induction that is I is directly proportional to B

not that there's B equation 2 by combining equations 1 & 2

we get AI is proportional to B naught by T [Music]

this equation can be written as I is equal to C into B naught by T see is the proportionality constant

let this be equation three we know that B naught is equal to MU naught each

let this be equation for we also know that the ratio of magnetization to magnetic intensity is

magnetic susceptibility that is Chi is equal to I by age at this the equation five

substituting equation four and five in equation three and on simplification we get chi is

equal to C into mu naught by T [Music] this is known as Curie's law

where C is called Curie's constant let this be equation six does the magnetic susceptibility Chi

depends on the nature and the temperature of the material since the magnetization of a material is

directly proportional to the applied magnetic field induction and inversely proportional to its absolute temperature

the magnetization of a material increases up to a certain level by increasing the magnetic field and

decreasing the temperature at this magnetization all the atomic dipoles are aligned in

the same direction of the magnetic field this value of magnetization is known as saturation value

and is represented as I s beyond this value Curie's law is not applicable

let us now discuss about ferromagnetic materials ferromagnetic materials are the

materials that are strongly attracted by the magnets when a borrow Farrow

material is placed in a non-uniform external magnetic field it has a strong tendency to move from a

region of weak magnetic field to a stronger magnetic field and the field lines are highly

concentrated inside the ferromagnetic material let us discuss the causes of

ferromagnetism similar to the paramagnetic material the individual atoms in a ferromagnetic

material also possess a permanent magnetic dipole moment due to the orbiting electrons

these individual atoms interact with one another and arrange themselves in a common direction over the volume of some

millimeters this volume is called the domain each domain contains about 10 to the

power 11 atoms and each domain has a net magnetization the magnetization changes from domain to

domain does the net magnetization of a ferromagnetic material is negligible

when about a ferromagnetic material is placed in an external magnetic field of induction be not

the magnetization of the dough means orient in the direction of the applied magnetic field

when the external magnetic field is removed some ferromagnetic materials can retain

the magnetization and such materials are called hard ferromagnets or hard magnetic materials

Nicole Steele takuna etc are the examples of hard ferromagnetic materials these materials are used to prepare

permanent magnets there are some other materials which can lose its magnetization when the external

magnetic field is removed these materials are called soft ferromagnetic materials and they are

used to prepare temporary magnets iein cobalt

etc are the examples of soft ferromagnetic materials the magnetic susceptibility of

ferromagnetic materials is positive and very much greater than one the relative magnetic permeability of

these materials is also positive and very much greater than one now

let us discuss an activity to know the effect of temperature on ferromagnetism that is consider an l-shaped wooden

stand and fix a strong magnet on top of it consider a ferromagnetic material say a

nickle paperclip tied to a string which is fixed at the base of the wooden stamp let the paperclip be suspended in air

with the help of a magnet as shown now heat the clip with a lighter to increase its temperature

at a particular temperature the paper-clipped falls down that is

at that temperature the clip transforms from being ferromagnetic to paramagnetic

this transition temperature is known as Curie's temperature in other words

temperature of transition from ferromagnetic to paramagnetic is called QD temperature and is denoted by TC

the magnetic susceptibility above cue Lee's temperature which is in the paramagnetic phase is given as Chi is

equal to C by t minus TC this table lists out Curie's temperature of some ferromagnetic materials

let us now discuss about his terraces of a ferromagnetic substance the relation between the magnetic field

induction B and the magnetic intensity or applied magnetic field H is complex and is often nonlinear

to understand this consider an unmagnetized ferromagnetic material in the core of a current-carrying solenoid

let us see the magnetic behavior of the ferromagnetic material through one cycle of magnetization by plotting a graph

with H on the x-axis and B on the y-axis when the current passing through the solenoid increases the magnetic field in

the core of the solenoid H also increases as a result

magnetic field strength be in the ferromagnetic material placed in the solenoid also increases

this is represented by the curve Opie in the craft which shows the alignment and merger of

domains and no further enhancement is possible after this by reducing the current through the

solenoid the applied magnetic field H decreases to zero when H is equal to zero

the magnetic field strength in the ferromagnetic material B is not equal to zero and this is represented by the

curve BQ in the graph and the value of b @h is equal to 0 is called retentive 80 or remanence

now increase the current through the solenoid in a direction reverse to that of the previous one

does certain domains in the ferromagnetic material are flipped until the net field inside it stands nullified

this is represented by the curve Q R in the graph this magnitude of applied magnetic field

H is known as coercivity as the current in the reverse direction

increases and magnitude we once again obtain the saturation magnetization in a direction opposite to

that of the previous one this is represented by the curve RS in the graph

again decrease the magnitude of current in the reverse direction such that the applied

magnetic field H also decreases and becomes zero but the magnetic field strength in the

ferromagnetic material is not zero this is represented by s T in the graph again

decrease the magnitude of current in the reverse direction such that the applied magnetic field H also decreases and

becomes zero but the magnetic field strength in the ferromagnetic material is not zero

this is represented by s T in the graph and finally increase the current in the original direction then again the

magnetic domains in the ferromagnetic material slipped until the net magnetic field inside it becomes zero

the magnetic field thus increases in the original direction this is represented by tu in the graph

with any further increase in current through the solenoid the applied magnetic field in it and the magnetic

field strength in the ferromagnetic material increases to its saturation value

this is represented by you P in the graph we can observe that the curve or P does

not retrace itself as the magnetic intensity or applied magnetic field H is reduced

hence we can say that for a given value of magnetic intensity H magnetic field B depends on the previous history of the

sample this phenomenon is called hysteresis magnetic flux is the physical quantity

that gives the measure of the strength of a magnetic field over a given area magnetic flux is defined as the number

of magnetic field lines passing through a given area in a magnetic field the magnetic flux Phi is equal to B dot

a which is equal to B a cos theta where B is the strength of the magnetic field

e is the area of the given surface through which the field lines pass and theta is the angle between the

direction of magnetic field and the area vector let this be equation 1 the SI unit of

magnetic flux is Weber and it's CGS unit is Maxwell maximum magnetic flux passes through a

given area when the area vector and the magnetic field are in the same direction that is the angle between the plane of

the given area and the magnetic field is 90 degree angle between the area vector and the

magnetic field theta is equal to 0 degree course 0 degree is equal to 1 does the magnetic flux Phi is equal to

BA when the flux passing through a given area is maximum the magnetic flux

passing per unit area is called magnetic flux density the magnetic flux density B is equal to

Phi by a that this V equation two now let's discuss about Gauss law for

magnetism we know that God's law for electrostatics is derived from Coulomb's

law from Coulomb's law of electrostatics we derive that the electric field strength

e is equal to 1 by 4 pie epsilon-not into Q by R square

let this be equation three Gauss law for electrostatics states that the electric flux passing through a

closed surface is equal to 1 by epsilon naught times the total charge enclosed by the closed surface

that is integral over the closed surface a dot d s is equal to Q by epsilon not here integral over the closed surface ee

dot d s is the electric flux ad Q is the total charge enclosed by the closed surface

let this be equation for similarly Gauss law for magnetism can be derived from the definition of magnetic

field strength we know that the magnetic field strength B is equal to MU naught by 4 PI into M

by r square let this be equation five by observing the Gauss law for

electrostatics we can write Gauss law for magnetism as integral over a closed surface b dot d s is equal to MU knot

times the net bolt strength enclosed by the closed surface here integral over the closed surface b

dot d s is the magnetic flux and M is the total pole strength enclosed by the closed surface

since the isolated magnetic pole or magnetic monopole does not exist that is the magnetic dipoles alone exist with

the poles that are opposite in nature the netball strength enclosed by the closed surface is zero

now we can write Gauss law for magnetism as integral over the closed surface b dot d

s is equal to zero let this be equation six let's discuss coleslaw for

electrostatics and magnetism more explicitly by considering the field lines due to an electric dipole and a

magnetic dipole consider a closed surface that encloses one of the charges of an electric dipole

and another closed surface which encloses one of the poles of a bow magnet

in case of an electric dipole the electric field lines begin on the positive charge and end on the negative

charge that is the electric field lines are not closed loops they are open curves

here the electric field lines go beyond the closed surface does a non-0 electric flux exists in a

closed surface electric flux is equal to 1 by epsilon not times the charge enclosed by the

closed surface on the other hand the magnetic field lines due to a magnetic dipole are

directed from North Pole to South Pole externally and South Pole to North Pole internally

that is the magnetic field lines are continuous closed loops here the number of magnetic field lines

going beyond the closed surface is equal to the number of magnetic field lines entering into the closed surface

thus the net magnetic flux enclosed by the closed surface is zero for a better understanding let's discuss

Gauss law for magnetism with some examples such as a solenoid and a toroid in the case of a current-carrying

solenoid the magnetic field lines around the current-carrying solenoid are similar to

that of the magnetic field lines due to a magnetic dipole here the magnetic field lines come out

from one face of the solenoid and enter into its other face let's consider a closed surface around

one face of the solenoid then the number of magnetic field lines going out of the closed surface is equal

to the number of magnetic field lines coming in to the closed surface does the net magnetic flux enclosed by

the closed surface is equal to zero in our other example that is of a toroid the current-carrying

toroid produces a magnetic field at its core in circular loops now consider a closed surface around the

point of the toroid as the magnetic field lines due to the current carrying tore out a continuous

closed loops the number of magnetic field lines going out of the closed surface is equal to the number of

magnetic field lines coming into the closed surface does the net magnetic flux enclosed by the closed surface is

equal to zero magnetic flux is the physical quantity that gives the measure of the strength

of a magnetic field over a given area magnetic flux is defined as the number of magnetic field lines passing through

a given area in a magnetic field the magnetic flux Phi is equal to B dot a which is equal to B a cos theta

where B is the strength of the magnetic field e is the area of the given surface

through which the field lines pass and theta is the angle between the direction of magnetic field and the area

vector let this be equation 1 the SI unit of magnetic flux is Weber

and it's CGS unit is Maxwell maximum magnetic flux passes through a given area when the area vector and the

magnetic field are in the same direction that is the angle between the plane of the given area and the magnetic field is

90 degree the angle between the area vector and the magnetic field theta is equal to 0

degree course 0 degree is equal to 1 does the magnetic flux Phi is equal to BA

when the flux passing through a given area is maximum the magnetic flux passing per unit area is called magnetic

flux density then the magnetic flux density B is equal to Phi by a let this be equation 2

now let's discuss about Gauss law for magnetism we know that God's law for

electrostatics is derived from Coulomb's law from Coulomb's law of electrostatics we

derive that the electric field strength e is equal to 1 by 4 pie epsilon-not into

Q by R square let this be equation three Gauss law for electrostatics states that

the electric flux passing through a closed surface is equal to 1 by epsilon naught times the total charge enclosed

by the closed surface that is integral over the closed surface a dot d s is equal to Q by epsilon not

here integral over the closed surface a dot d s is the electric flux at Q is the total charge enclosed by the closed

surface let this be equation for similarly Gauss law for magnetism can be

derived from the definition of magnetic field strength we know that the magnetic field strength

B is equal to MU knot by 4 PI into M by r square let this be equation five

by observing the Gauss law for electrostatics we can write Gauss law for magnetism as integral over a closed

surface b dot d s is equal to MU knot times the net bolt strength enclosed by the closed surface

here integral over the closed surface b dot d s is the magnetic flux and M is the total pole strength enclosed by the

closed surface since the isolated magnetic pole or magnetic monopole does not exist that is

the magnetic dipoles alone exist with the poles that are opposite in nature the netball strength enclosed by the

closed surface is zero now we can dry two Gauss law for magnetism as

integral over the closed surface b dot d s is equal to zero let this be equation six

let's discuss coleslaw for electrostatics and magnetism more explicitly by considering the field

lines due to an electric dipole and a magnetic dipole consider a closed surface that encloses one of the charges

of an electric dipole and another closed surface which encloses one of the poles of a bow

magnet in case of an electric dipole the electric field lines begin on the

positive charge and end on the negative charge that is the electric field lines are not

closed loops they are open curves here the electric field lines go beyond the closed surface

does a non-0 electric flux exists in a closed surface electric flux is equal to one by epsilon

not two means the charge enclosed by the closed surface on the other hand the magnetic field

lines due to a magnetic dipole are directed from North Pole to South Pole externally and South Pole to North Pole

internally that is the magnetic field lines are continuous closed loops

here the number of magnetic field lines going beyond the closed surface is equal to the number of magnetic field lines

entering into the closed surface thus the net magnetic flux enclosed by the closed surface is zero

for a better understanding let's discuss Gauss law for magnetism with some examples such as a solenoid and a toroid

in the case of a current-carrying solenoid the magnetic field lines around the

current-carrying solenoid are similar to that of the magnetic field lines due to a magnetic dipole

here the magnetic field lines come out from one face of the solenoid and enter into its other face

let's consider a closed surface around one face of the solenoid then the number of magnetic field lines

going out of the closed surface is equal to the number of magnetic field lines coming in to the closed surface

thus the net magnetic flux enclosed by the closed surface is equal to zero in our other example

[Music] that is of a toroid the current-carrying toroid produces a magnetic field at its

core in circular loops now consider a closed surface around a point of the toroid

as the magnetic field lines due to the current carrying tore out a continuous closed flutes the number of magnetic

field lines going out of the closed surface is equal to the number of magnetic field lines coming in to the

closed surface thus the net magnetic flux enclosed by the closed surface is equal to zero

earth is a natural source of magnetism the strength of the Earth's magnetic field varies from place to place on the

surface of the earth the magnitude of the Earth's magnetic field strength is off the order 10 power

minus five Tesla the actual cause of the Earth's magnetic field is not yet known

as of now it is believed that the Earth's magnetic field is caused due to the convective

motion of metallic fluids in the outer core of the earth iron and nickel formed the major

components of the fluids in motion the convective motion of these fluids gives rise to electrical currents

which in turn give rise to the Earth's magnetism this is known as the dynamo effect

the Earth's magnetism can be realized by its magnetic field lines the Earth's magnetic field lines are similar to the

magnetic field lines of a magnetic dipole hence we can assume a magnetic dipole to

be placed at the center of the earth however the axis of the hypothetical magnetic dipole assumed at the center of

the earth does not coincide with that of the geographic axis of the earth about which it rotates

the angle between the axis of the dipole and the geographic axis of the earth is approximately eleven point five degree

from the observation of the Earth's magnetic field lines we can see that the magnetic poles are located where the

field lines due to the dipole enter or leave the earth a magnetic pole is located at latitude

of seventy nine point seven four degree knot and a longitude of seventy one point eight degree west

this is a place in not Canada this pool which is near the geographic North Pole is called the not magnetic

pole Earth's magnetic field lines enter the earth near this pole

another magnetic pole is located at latitude of seventy nine point seven four degrees south and longitude of 108

point two two degree east a place in the Antarctica this pool which is located near the

geographic South Pole is called the South Magnetic Pole Earth's magnetic field lines leave the

earth near this sport when compared with the magnetic field lines of a bar magnet this nomenclature

of the magnetic poles of the Earth's magnetic field creates confusion this is because for the bar magnet the

feed lines enter the magnet added South Pole and leave the magnet at its North Pole

whereas for the earth the field lines go into the earth at it's not magnetic pool and come out of the earth added South

Magnetic Pole the convention for this nomenclature for the Earth's magnetic field a ruse due to

the fact that the North Pole of a freely suspended bar magnet points towards the geographic not whereas the South Pole of

the magnet points towards the geographic south the north pole of a magnet was named so

because it is a not seeking pole similarly the south pole of a magnet was named so

because it is a salt seeking pool we know that light poles repel and unlike poles attract

in reality the North Magnetic Pole of the earth behaves like a South Pole and the South Magnetic Pole of the earth

behaves like a North Pole to completely describe the magnetic field at any point on the surface of the

earth we have to specify its three elements at that point namely detonation d

angle of dip or inclination I and horizontal component of the Earth's magnetic field H E

let us study about these three elements in detail one by one first

the declination we all know that the earth is spherical in shape on this spherical surface

we can draw an infinite number of imaginary circles passing through the Earth's geographical not and South Poles

all these circles have one common diameter which is the line joining the

geographical North and South Poles or the Earth's axis of rotation these imaginary circles are called

longitudes each of these circles along with the Earth's axis of rotation

can be drawn in one plane this plane is called the geographic meridian

the geographical meridian when viewed from top appears to be a straight line similarly

we can obtain the magnetic Meridian by drawing a line from the magnetic north and south poles this magnetic meridian

also looks like a straight line when viewed from the top of the chosen point at any given point

the geographical meridian and the magnetic meridian together look like two intersecting straight lines

the acute angle between these two straight lines is known as declination it is denoted by the capital letter D

declination changes from place to place on earth declination is minimal at the equator and goes on increasing with

latitude the second element of the Earth's magnetic field is the angle of dip or

inclination a magnetic compass needle is provided with the pivot such that it can rotate freely about a vertical axis

the needle comes to rest when aligned with the magnetic Meridian to indicate the magnetic north

if the needy were also provided with the pivot such that it can rotate freely about a horizontal axis

it would also rotate in the magnetic meridian clean if the campus is placed in the northern

hemisphere it's not the end dips down from the horizontal position if the compass is

placed in the southern hemisphere it's out and dips down from the horizontal

the angle through which it dips with respect to the horizontal plane at that point is known as the angle of dip or

the inclination denoted by the captor letter I in other words inclination is the angle

that the total magnetic field of the earth de

makes with the horizontal surface of the earth at a given point the inclination is zero at the equator

and increases as the latitude increases if this compass is placed atop the magnetic pole

it will come to rest in the vertical position we can measure the inclination at any given point using a magnetic

needle with the horizontal axis and a spirit level the study of these elements helped us to

find the total magnetic field of the earth be2 find B e at any point on the earth

we take the help of the third element the horizontal component of the Earth's magnetic field

H E at that point be e and H E are vectors

let us now construct the vector diagram using all the three elements locate point B on the globe at which you

want to determine the Earth's total magnetic field de

draw a circle passing through the point P and the geographic North and South Poles

this is the geographic meridian circle draw another circle passing through the point P and the magnetic north and south

poles this is the magnetic Meridian circle draw a plane which is tangential to the

sphere at point B draw a tangent de to the geographic meridian circle at point B

pa lies on the tangent plane and represents the geographic north south direction draw a tangent DB to the

magnetic meridian circle at Point P Bibi also lies on the tangent plane but represents the magnetic north south

direction construct a parallelepiped passing through P a and B rotate the line te in the tangent plane

such that it touches the pad lilo piped at B this angle of rotation is the angle of

declination D at the point P the length of the line PB to some scale represents the magnitude of the

horizontal component H of the Earth's magnetic field at the point P rotate the line PB in the vertical plane such that

it touches the parallelepiped at sea this angle of rotation is the angle of dip I

at the point be the line PC represents the magnitude and direction of the total magnetic field B

II at the point B drawing this three-dimensional diagram is a cumbersome process

instead we can draw a two-dimensional view of the essential elements to determine the Earth's total magnetic

field take only the plane represented by B BCD in the three dimensional view and draw a two dimensional view of triangle

PBC draw a horizontal line PB with the arrow head at B the length of this line to some scale

represents the magnitude of H II draw a line PC making an angle I with PB draw a line BC is perpendicular to the line PB

with an arrowhead at sea line BC represents the vertical component ve of the Earth's magnetic

field on the line PC put an arrowhead at sea line PC represents the total magnetic

field B II of the earth at the point B we can now write the trigonometric relationships for the sides and the

angle in the right angled triangle sine I is equal to BC / BC which is equal to ve / b e or ve is equal to b e

sine i Gosai is equal to PD / PC is equal to h e / b e or h e is equal to b e cos i

ten-eye is equal to BC divided by PB is equal to ve divided by H E or ve is equal to H eat an eye

let us start with some general facts related to magnets a freely suspended bar magnet oscillates

for some time and then comes to rest along the magnetic Meridian in the direction of geographic north and south

one end of the magnet points to the geographic North Pole called not seeking pool or not Pole of the magnet

and the other end points to the geographic South Pole called salt seeking pool or South Pole

of the magnet this is because the earth behaves as a huge bar magnet with its magnetic north

pole located near the geographic South Pole and with its magnetic South Pole located near the geographic North Pole

we know that the light poles of two magnets repel each other and the unlike poles attract each other does the North

Pole of the magnet is attracted by the Earth's magnetic South Pole and vice-versa

if a bar magnet is broken into two pieces we get two similar magnets with the

decrease in the magnitude of their properties thus the magnets always exist in dipoles

isolated magnetic monopoles do not exist this implies that isolated magnetic north pole or South Pole does not exist

let us now discuss an activity about the magnetic field lines of a bar magnet consider a glass sheet with some iron

filings sprinkled on it bring the power magnet from the bottom of the glass sheet close to the sheet as the magnet

is brought close to the glass sheet we observe that the iron filings on the sheet arrange themselves as shown

if we draw lines along the orientation of the iron filings the lines will represent the magnetic field lines

similar field lines are observed in the case of a current-carrying solenoid and an electric dipole

let us now learn about the properties of magnetic field lines around a bar magnet the field lines of a magnet start from

the North Pole and end at the South Pole externally which is outside the magnet but internally that is inside the magnet

the magnetic field lines start from the South Pole and end at the North Pole does the magnetic field lines of a

magnetic dipole are continuous closed loops in the case of an electric dipole the

electric field lines start from the positive charge and end at the negative charge

unlike magnetic field lines the electric field lines are not closed loops they are open curves

the felines give us a visual impression of the magnetic field if we draw a tangent to a magnetic field

line at a given point it represents the direction of resultant magnetic field at that point

magnetic field lines never intersect each other because the resultant magnetic field at

a point has only one direction if we assume the two magnetic field lines intersect at a point then the

resultant magnetic field at that point would have two different directions which is not possible

the magnitude of magnetic induction which gives the strength of the magnetic field is obtained by the number of field

lines passing normally through a given area if the number of field lines passing

normally true a given area is large then the field is considered to be strong it is similar to strength of an electric

field if the number of field lines passing normally through the area is less then

the magnetic field is considered to be weak an alternative method of plotting the

field lines of a magnetic dipole is as follows take a bar magnet which is nothing but a

magnetic dipole and place it on a sheet of paper which is placed on a horizontal surface

then place a small magnetic compass at the North Pole of the magnet plot a point on the paper indicating

knot of the compass needle shift the compass such that the south of the compass needle is observed at the

plotted point then again plot another point at the knot of the compass needle and then

shift the compass as done earlier repeat the process to plot different points on the sheet around the magnet

and note down the orientation of the compass at each position we observe that the series of points

plotted on the sheet are directed from the North Pole of the magnet to its South Pole

by connecting all the points we get the magnetic field lines due to the magnetic dipole the direction of the compass at

different points on the field lines gives the direction of magnetic field at that point

let us now learn the similarities between a bar magnet and a solenoid by comparing the magnetic induction of both

finite number of continues turns of a conducting wire wound and helical shape represents a solenoid we learnt earlier

that the magnetic field lines of a bar magnet are similar to the field lines of the solenoid

hence a bar magnet can be assumed to be the same as a large number of current-carrying loops placed adjacent

to each other the two phases of the solenoid are similar to the poles of a bar magnet

the felines leave one face of the solenoid into its exterior and hence this face of the solenoid is liked not

pole of the bar magnet the field lines enter the solenoid at the other face and hence this face is like the South Pole

of the bar magnet does the magnetic fields lines of a solenoid are continuous closed loops

similar to the field lines in the case of a bar magnet we learnt earlier that if a bar magnet is cut into two pieces

perpendicular to its length two small bar magnets are formed similarly if a solenoid is cut

perpendicular to its length into two parts two solenoids of smaller lengths are

obtained the two solenoids produce weak magnetic fields around them

thus each smaller solenoid acts like a small bar magnet to make it more clear that the field due

to a solenoid is similar to that of a bar magnet we calculate the magnetic field induction B at a distant point on

the axis of the solenoid and compare with the magnetic field induction at a point on the HCl line of a bar magnet

consider a solenoid of finite length with n turns per unit length let e be the radius

- L be the length and I be the current passing through the solenoid let the solenoid be placed such that the

axis of the solenoid is along the x axis of the coordinate system and its center coincides with the origin

then the left end of the solenoid lies at the position minus L and it's right end at plus L let us consider a point P

on the axis of the solenoid and let R be the distance from the center of the solenoid to that point to calculate the

magnetic field induction B at the point P on the axle line of the solenoid consider a small element of the solenoid

of thickness DX located at a distance of x from the center of the solenoid then the distance

of the point P from the small element of the solenoid is our minus X as n is the number of turns per unit length the

number of turns in the small element of the solenoid is equal to number of turns per unit length into length of the small

element of the solenoid that is equal to n into DX we learnt earlier that the magnetic

induction be on the axis of a current-carrying circular loop at a distance X from the center of the loop

is equal to mu knot I a square by 2 into X square plus a square whole part 3 by 2 thus the magnetic induction due to the

current passing through the small element of the solenoid at the point P on the XL line DB is equal to MU knot n

DX I a square by 2 into R minus X square plus a square whole power 3 by 2 the total magnetic induction due to the

solenoid can be calculated by dividing the total length of the solenoid into number of small elements and by

integrating the magnetic induction due to all the small elements we get the total magnetic induction due to the

solenoid when we consider the small elements of the solenoid from one end to the other

the distance of the elements from the center of the solenoid varies from minus L to L thus the total magnetic induction

at the point P due to the solenoid is B is equal to integral minus L to L DB that is equal to integral minus L to L

mu not n DX I a square by 2 into R minus X square plus a square all part 3 by 2 but I am and mu not are constant

hence the magnetic induction B is equal to MU knot ni a square by 2 into integral minus L to L DX by AR minus X

square plus a square whole part 3 by 2 when we consider the point on the axis of the solenoid at a large distance R is

much greater than a and R is much greater than X hence we neglect the terms e and X in

the denominator of the expression for B then B is equal to mu not n I ay square by 2 into integral minus L to L DX by

r-cube but the distance of the point P from the origin R is constant

thus B is equal to mu not n I ay square by 2 R cube into integral minus L to L DX on integrating and substituting the

limits we get the magnetic induction B is equal to MU not n I ay square by 2 R cube into 2 L by multiplying the

numerator and denominator of the expression with PI and rearranging the terms in the expression we get the

magnetic induction B is equal to MU naught by 2 pi into n i2 L PI a square by r cube

we learnt earlier that a current carrying loop behaves like a magnetic dipole and it's dipole moment is given

by M is equal to I into a where a is the area vector of the loop the solenoid consists of n number of loops per unit

length I is the current through the solenoid and II is the radius of each loop

thus area e of each loop of the solenoid is PI into a square the total number of loops in the

solenoid is n into 2 L and hence the magnetic moment of the solenoid M is equal to n 2 L I a which is equal to n 2

L I PI a square substituting M for the terms in the expression for magnetic induction B we get the magnetic

induction B is equal to MU naught by 2 pi into m by r cube on multiplying the numerator and denominator with 2

we get the magnetic induction B is equal to MU naught by 4 pi into 2 m by r cube this is the same expression that is used

to find the magnetic induction at a distant point from the center of a bar magnet on its axial line does a current

carrying solenoid and a power magnet traduce similar magnetic fields therefore a solenoid is equivalent to a

bar magnet and their magnetic moments are also equal if the magnitude of the induction they produce at given distant

points from their centers on their HC lines is equal the earth abounds with a variety of

elements and compounds in addition we have seen different types of alloys compounds and elements to

classify these substances based on their magnetic properties let us discuss the basics of magnetic properties

we know that matter is made of atoms and atoms are made of electrons and nuclei we have seen that a circulating electron

in an atom has a magnetic moment the resultant magnetic moment of an atom is the vector sum of the magnetic

moments of all such circulating electrons in the atom here the magnetic moments of these atoms in

an object are randomly oriented and then net magnetic moment is zero when the object is placed in an external

magnetic field the magnetic moments of the atoms are aligned partially or completely in the

direction of the applied magnetic field then the net magnetic moment of the object is in the direction of the

external magnetic field does the net magnetic moment per unit volume is called magnetization or

intensity of magnetization that is AI is equal to M by V the unit for intensity of magnetization

is ampere per meter it's dimensional formula is M 0 L minus 1 T 0 a 1

when an object is placed in an external magnetic field the total magnetic field inside the object is the sum of the

applied magnetic field and the magnetic field due to the magnetization of the object to discuss this more explicitly

let us consider a long current carrying solenoid we're be not is the magnetic field in

the interior of the solenoid due to the current passing through it when a magnetic material is inserted into the

solenoid the material gets magnetized you in such cases the total magnetic field

inside the material is the sum of magnetic field due to the current carrying solenoid and the magnetic field

due to the magnetization of the material that is B is equal to B naught plus BM where B is the total magnetic field

inside the material be not is the magnetic field due to the current carrying solenoid and B M is the

magnetic field due to the magnetization of the material let this be equation 1 the magnetic

field due to the magnetization of the material is directly proportional to its intensity of magnetization

that is BM is directly proportional to I this equation can be further written as BM is equal to MU naught into I where mu

naught is the magnetic permeability of vacuum let this be equation 2

now let us introduce a new vector quantity called magnetic intensity denoted by H where H is equal to B by mu

naught minus I let this be equation 3 the units and dimensions of magnetic intensity are the same as that of

intensity of magnetization that is the SI unit of H is ampere per meter and its dimensional formula is M 0 L minus 1 t 0

a one on rearranging the terms in equation three we get the total magnetic field inside the material B is equal to

MU naught into I plus h that this be equation for the total magnetic field inside the

material is redefined in terms of I and H that is the external magnetic field

applied on the material represented by H and the magnetic field due to the magnetization of the material

represented by AI the contribution due to the magnetization of the material I is

influenced by factors such as the nature of the material to be magnetized and the applied magnetic field

it can be expressed as I is equal to Chi into H that this be equation five

where chi is a dimensionless quantity called magnetic susceptibility it depends on the nature of the material

which represents the degree of magnetization in response to an external magnetic field

the value of magnetic susceptibility is small and positive for paramagnetic materials

it is small and negative for diamagnetic materials substituting equation five in equation 4

we get the total magnetic field inside the material B is equal to MU naught into Chi h plus h that is B is equal to

MU naught into 1 plus Chi into H let this be equation six but the magnetic susceptibility and relative

magnetic permeability are related as mu R is equal to 1 plus Chi hence in place of one plus Chi we can

write mu R and we can further write equation six as B is equal to MU naught into mu R into H

let this be equation seven we know that the relative magnetic permeability is the ratio of the

magnetic permeability of the material to the magnetic permeability of vacuum that is mu R is equal to mu by mu not

then mu is equal to MU not into mu R on substituting the magnetic permeability of the material mu in

equation seven we get the magnetic field as B is equal to new age let this be equation eight

the three quantities magnetic susceptibility magnetic permeability and relative

magnetic permeability are related to each other and only one of them is independent

if one of these values is given the other two values can be determined easily

let us have a look at the magnetic susceptibility of some elements at 300 Kelvin given in the following table

here it can be seen that in the case of diamagnetic substances the value of magnetic susceptibility is small and

negative and in the case of paramagnetic substances the value of magnetic

susceptibility is small and positive first let us learn about magnetic compass a magnetic compass or compass

needle is used to find the direction of a magnetic field at a given point in a horizontal plane

it essentially consists of a magnetic needle which is placed on a pivot in the

horizontal plane does a magnetic compass can move only in a horizontal plane

when the magnetic compass is placed in a horizontal plane on Earth's surface it aligns itself along the direction of the

horizontal component of the Earth's magnetic field at that point or it can be said that the needle aligns

itself along the magnetic Meridian at that point at some places the deposits of magnetic

materials inside the earth cause the magnetic compass to deviate from the magnetic meridian

you at such locations the angle of declination at that point helps us to

determine the actual direction of the north that is now discussed the deflection of

a magnetic compass placed at either of the two magnetic poles of the earth at the polls

the magnetic field lines either converge or diverge vertically hence the horizontal component of the

magnetic field is negligible this means that the needle can effectively point in any direction

thus in terms of the pathfinding ability the compasses rendered useless at the pawns

in such cases a dip circle is useful dip circle is basically a magnetic needle pivoted in such a manner that it

is free to move in a vertical plane we can thus measure the angle made by the magnetic field with the horizontal plane

in the case of polls this needle points downward and as it approaches the equator the needle aligns in the

horizontal direction it has now discuss about the Earth's magnetic field the Earth's magnetism is

largely attributed to iron and nickel ions present in the hot and molten core of the earth

this theory gains force from the fact that the moon does not have a molten core and hence it does not have a

magnetic field you Venus has a slower rate of rotation and

a weaker magnetic field compared to Jupiter which has the fastest rate of rotation and very powerful magnetic

field although magnetism is attributed to these circulating currents in the core

of the planets the energy required for sustaining these currents and the causes for this is not

very well understood till date these are still interesting research topics

in fact the part of the solar wind that is the stream of charged particles emitted from the Sun produces some

magnetic field which interacts with the Earth's magnetic field therefore you can say that the Earth's

magnetic field influences the solar wind the pattern of the Earth's magnetic field is noticeably different at the

poles than from the rest of the earth in fact there is evidence that the Earth's magnetic field changes prominently in

the short term which is in centuries and long term which is over a span of a million years

the dip angle at London varied by 3.5 degrees in the span of 240 years that is from 1582 18 2080

this indicates that the position of the Earth's magnetic poles varies its position with time

hence it is observed that the Earth's magnetic field has even reversed the direction during long term changes

let's begin with permanent magnets permanent magnets are substances that can retain its ferromagnetic property

for a long period of time at room temperature let's discuss the properties of a

material used for making a permanent magnet we cannot make permanent magnets from

all types of materials the hysteresis curve helps us to select a suitable material for it

the material should have high retentive 'ti in order to retain its magnetization for the long period of time and increase

the strength of the magnet the material should have high coercivity so that it does not lose the magnetic

property during temperature fluctuations unwanted or scattered magnetic fields and minor mechanical damage

the material should have a high relative magnetic permeability so that it can be easily magnetized

does taking into consideration of all the properties steel is the most suitable choice

the other suitable materials are alnico cobalt steel and tea Conal there are different methods of making

permanent magnets in method one we can prepare a permanent magnet by holding a steel rod in the

north-south direction and hammering it repeatedly this is an age-old method of

magnetization in meta too all the steel rod and rub it with one

end of a bar magnet repeatedly in a particular direction does

abundant magnet is formed this method of magnetization is known as single touch method

however the most efficient method of making a permanent magnet is to place a suitable magnetic material in the core

of a solenoid and pass direct current through it does

magnetic field due to the current carrying solenoid magnetizes the material placed in the core of the

solenoid this method of magnetization is known as electrical method

permanent magnets have many applications such as in magnetic door stoppers and magnetic screwdrivers

you now let's discuss the making of electromagnets

the materials used in electromagnets should have high magnetic relative permeability and low written tivity

however the hysteresis loop for this type of material is narrow

considering all these properties softn is the most suitable material for making electromagnets

place a soft iron jaunt in the core of the solenoid and pass current through it the magnetism of the solenoid increases

by many times due to the soft iron rod in the core of the solenoid when the current through the solenoid is

switched off the magnetism due to the solenoid is also switched off because of load ten

tivity of soft iron does the electromagnets are referred to as temporary magnets

electromagnets have their usage in many applications such as electric Bell loud speakers

and telephone diaphragms huge electromagnets are used in cranes to lift bulk quantities of iron steel

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