VAN DE GRAaFF VAN DE GRAaFF GENERATORGENERATOR

CAPACITORSCAPACITORSDIELECTRICSDIELECTRICS

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Van de graaff generator Van de graaff generator

Capacitors Capacitors

dielectrics dielectrics

Click the topic you Click the topic you want to see.want to see.Principle of VAN DE GRAAFF GENEPrinciple of VAN DE GRAAFF GENE

RATORRATORCONSTRUCTION AND WORKING OFCONSTRUCTION AND WORKING OF

VAN DE GRAAFF GENERATOR VAN DE GRAAFF GENERATOR

PRINCIPLE OF VAN DE GRAAFF PRINCIPLE OF VAN DE GRAAFF GENERATOR GENERATOR

It is based on the following two It is based on the following two electrostatic phenomena :electrostatic phenomena :

1. The electric discharge takes place in air 1. The electric discharge takes place in air or gases readily at pointed conductors.or gases readily at pointed conductors.

2. If a hollow conductor is in contact with an 2. If a hollow conductor is in contact with an other conductor, then as charge is other conductor, then as charge is supplied to the conductor, the hollow supplied to the conductor, the hollow conductor accepting the charge conductor accepting the charge irrespective of the fact, howsoever large irrespective of the fact, howsoever large its potential may grow. The charge its potential may grow. The charge immediately shifts to outer surface of the immediately shifts to outer surface of the hollow conductor. hollow conductor.

Van De Graaff Van De Graaff Generator consists of a large Generator consists of a large hollow metallic sphere S hollow metallic sphere S mounted on two insulating mounted on two insulating columns CC’ as shown in the columns CC’ as shown in the diagram. An endless belt of diagram. An endless belt of an insulating material is made an insulating material is made to run on two pulleys Pto run on two pulleys P1 1 and and

PP2 2 with the help of an electric with the help of an electric

motor. The metal comb Cmotor. The metal comb C1 1 , ,

called spray comb is held near called spray comb is held near the lower end of thethe lower end of the

VAN DE GRAAFF VAN DE GRAAFF GENERATORGENERATOR

belt. When the spray comb is maintained at high belt. When the spray comb is maintained at high positivepositive

potential with the help of E.H.T. source(≈10 potential with the help of E.H.T. source(≈10 4 4 V ), it V ), it produces ions in the vicinity. The positive produces ions in the vicinity. The positive ions get sprayed on the belt due to the repulsive ions get sprayed on the belt due to the repulsive action of comb Caction of comb C1 1 , which are carried upward by the , which are carried upward by the

moving belt. A comb Cmoving belt. A comb C22 , , called collecting comb is called collecting comb is

positioned near the upper end of the belt, such that positioned near the upper end of the belt, such that the pointed ends touch belt and the other end is in the pointed ends touch belt and the other end is in contact with the inner surface of the metallic sphere S. contact with the inner surface of the metallic sphere S. The comb CThe comb C22 collects the positive ions and transfers collects the positive ions and transfers

them to the metallic sphere. The charge transferred by them to the metallic sphere. The charge transferred by the comb Cthe comb C22 immediately moves on the outer surface immediately moves on the outer surface

of the hollow sphere. As the belt goes on moving, the of the hollow sphere. As the belt goes on moving, the accumulation of the positive charge on the sphere also accumulation of the positive charge on the sphere also keeps keeps

on taking place continuously and its on taking place continuously and its potential rises considerably with the potential rises considerably with the increase of charge on the sphere, its increase of charge on the sphere, its leakage due to ionisation of surroundings leakage due to ionisation of surroundings air also becomes faster. The maximum air also becomes faster. The maximum potential to which the sphere can be raised potential to which the sphere can be raised is reached, when the rate of loss of charge is reached, when the rate of loss of charge due to leakage becomes equal to the rate at due to leakage becomes equal to the rate at which charge is transferred to the sphere. which charge is transferred to the sphere. To prevent the leakage of the charge from To prevent the leakage of the charge from the sphere, the generator is completely the sphere, the generator is completely enclosed inside an earth connected steel enclosed inside an earth connected steel tank, which is filled with air under pressure. tank, which is filled with air under pressure.

if the projectiles, such as if the projectiles, such as protons, protons,

deutrons, etc. are generated in the deutrons, etc. are generated in the discharge tube D. With lower end discharge tube D. With lower end earthed and upper end inside the earthed and upper end inside the hollow sphere, they get accelerated hollow sphere, they get accelerated in downward direction along the in downward direction along the length of the tube. At the other end, length of the tube. At the other end, they come to heat the target with they come to heat the target with large kinetic energy and bring about large kinetic energy and bring about nuclear disintegration.nuclear disintegration.

This machine can This machine can generate high energy beams in the generate high energy beams in the range of 10 MeV or so.range of 10 MeV or so.

Click the topic which Click the topic which youyou want to want to see.see.Definition and advantage of capacitorsDefinition and advantage of capacitors

over conductors over conductorsPrinciple of capacitors Principle of capacitors TYPES OF CAPACITORSTYPES OF CAPACITORSGrouping or combination of capacitorsGrouping or combination of capacitorsEnergy stored in a charged capacitorEnergy stored in a charged capacitor

CAPACITORSCAPACITORS: : A capacitor is a device A capacitor is a device for storing a large quantity of electric for storing a large quantity of electric

charge. charge.

Advantage of capacitors over Advantage of capacitors over conductorsconductors::

A conductor can store a small A conductor can store a small amount of charge and hence it amount of charge and hence it possesses a small capacitance. To possesses a small capacitance. To store a large amount of store a large amount of

charge, two (or more) charge, two (or more) conductors are arranged to form conductors are arranged to form a capacitor. Thus, a capacitor a capacitor. Thus, a capacitor possesses a large capacitance to possesses a large capacitance to store charge and that too in a store charge and that too in a small space. small space.

To understand the To understand the principle of a capacitor, principle of a capacitor, consider an insulated consider an insulated plate A. Suppose that it plate A. Suppose that it is given positive charge is given positive charge ,till its potential ,till its potential becomes maximum. becomes maximum. The metal plate will not The metal plate will not hold any more charge hold any more charge over it. If charge is over it. If charge is given to the metalgiven to the metal

A SYSTEM OF A SYSTEM OF CONDUCTORS CONDUCTORS FORMS A FORMS A CAPACITORCAPACITOR

plate A, it will leak to the surroundings. plate A, it will leak to the surroundings. Now, place other metallic plate B near plate Now, place other metallic plate B near plate A. Due to induction, negative charge will A. Due to induction, negative charge will induced on the nearer face of plate B and induced on the nearer face of plate B and positive charges on its farther face as shown positive charges on its farther face as shown in diagram. The potential of plate A gets in diagram. The potential of plate A gets lowered due to induced negative charge on lowered due to induced negative charge on plate B and a bit raised due to the induced plate B and a bit raised due to the induced of positive charge. Since some metal plates of positive charge. Since some metal plates have finite thickness, induced negative have finite thickness, induced negative charge is nearer to plate A then the induced charge is nearer to plate A then the induced positive charge on plate B is. Therefore, on positive charge on plate B is. Therefore, on the whole, potential of plate A gets lowered, the whole, potential of plate A gets lowered, though be a very small amount. In order to though be a very small amount. In order to make the potential of the metal plate A make the potential of the metal plate A again the same, an additional small amount again the same, an additional small amount of charge has to of charge has to

be given to plate A. It indicates that be given to plate A. It indicates that the capacitance of a conductor the capacitance of a conductor increases by a small amount, when increases by a small amount, when another uncharged conductor is another uncharged conductor is placed near it. placed near it.

Now, connect the Now, connect the metal plate B to the earth as shownmetal plate B to the earth as shown

in diagram. The induced in diagram. The induced positive charge on plate B positive charge on plate B will immediately flow to will immediately flow to the earth as it is repelled by the earth as it is repelled by positive charge on plate A. positive charge on plate A. However, the inducedHowever, the induced

CAPACITORCAPACITOR

negative charge on plate B will stay on it. negative charge on plate B will stay on it. It does not flow to earth as it is attracted It does not flow to earth as it is attracted by positive charge on plate A. Thus, the by positive charge on plate A. Thus, the metal plate B will have only negative metal plate B will have only negative charge after being connected to earth. charge after being connected to earth. Due to the induced negative charge on Due to the induced negative charge on plate B, the potential of A will get lowered plate B, the potential of A will get lowered by a large amount. In order to raise the by a large amount. In order to raise the metal plate A again to the same potential, metal plate A again to the same potential, a large amount of charge has to be given a large amount of charge has to be given to it. Thus, it follows that the capacitance to it. Thus, it follows that the capacitance of a conductor gets increased greatly of a conductor gets increased greatly when an earth connected when an earth connected

conductor is placed near it. It forms conductor is placed near it. It forms the capacitor an such a arrangement the capacitor an such a arrangement of two metal plates is called a of two metal plates is called a capacitor.capacitor.

An arrangement of two An arrangement of two metallic conductors, so that when one metallic conductors, so that when one conductor is connected to the earth; the conductor is connected to the earth; the other conductor has the ability to store a other conductor has the ability to store a large amount of charge on it, is called a large amount of charge on it, is called a capacitor. capacitor.

TYPES OF TYPES OF CAPACITORSCAPACITORS PARALLEL PLATE CAPACITORPARALLEL PLATE CAPACITORSPHERICAL CAPACITORSPHERICAL CAPACITORCYLINDRICAL CAPACITORCYLINDRICAL CAPACITOR

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In a parallel plate In a parallel plate capacitor, the capacitor, the fringing of electric fringing of electric field takes place field takes place near the edges of near the edges of the two plates. In the two plates. In order to minimize order to minimize the edge effects, the edge effects, the separation the separation between the plates between the plates is kept small.is kept small.

Electric field Electric field between the two between the two plates of a parallel plates of a parallel plate capacitor is plate capacitor is uniform.uniform.

PARALLEL PLATE PARALLEL PLATE CAPACITORCAPACITOR

Electric field Electric field between two between two coatings of a coatings of a spherical capacitor spherical capacitor is not uniform.is not uniform.

The smaller the The smaller the difference between difference between the radii of the two the radii of the two coatings of a coatings of a spherical spherical capacitor, greater capacitor, greater is its capacitance. is its capacitance.

SPHERICAL SPHERICAL CAPACITORCAPACITOR

A cylindrical capacitor A cylindrical capacitor consists of two coaxial consists of two coaxial cylindrical shells, such cylindrical shells, such that one shell is earthed that one shell is earthed and another shell is used and another shell is used to store charge on it. The to store charge on it. The two cylindrical shells two cylindrical shells have a vary small have a vary small spacing between them, spacing between them, which is filled with some which is filled with some dielectric medium. dielectric medium.

CYLINDRICAL CYLINDRICAL CAPACITORCAPACITOR

CAPACITORS IN SERIESCAPACITORS IN SERIESCAPACITORS IN PARALLELCAPACITORS IN PARALLEL

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In series combination of In series combination of capacitors,capacitors,

Charge on each capacitor Charge on each capacitor is same.is same.

Potential difference Potential difference across a capacitor is across a capacitor is inversely proportional to inversely proportional to its capacitance.its capacitance.

The equivalent The equivalent capacitance is less than capacitance is less than the capacitance of the the capacitance of the smaller capacitor.smaller capacitor.

Capacitor in Capacitor in seriesseries

The reciprocal of the resultant (equivalent) The reciprocal of the resultant (equivalent) capacitance of the series combination of a capacitance of the series combination of a number of capacitors is equal to the sum of number of capacitors is equal to the sum of reciprocal capacitances of individual reciprocal capacitances of individual capacitors.capacitors.

1/C = 1/C1/C = 1/C1 1 + 1/C+ 1/C22 + 1/C + 1/C3 3

( where, C = resultant capacitance and( where, C = resultant capacitance and

C1,C2,C3 = capacitance of C1,C2,C3 = capacitance of individual capacitors)individual capacitors)

In parallel combination In parallel combination of capacitors,of capacitors,

Potential difference across Potential difference across each capacitor is same.each capacitor is same.

Charge on a capacitor is Charge on a capacitor is proportional to its proportional to its capacitance.capacitance.

The equivalent capacitance The equivalent capacitance is greater than the is greater than the capacitor of the largest capacitor of the largest capacitor. capacitor.

Capacitor in Capacitor in parallelparallel

The resultant (equivalent) capacitance of The resultant (equivalent) capacitance of the parallel combination of a number of the parallel combination of a number of capacitors is equal to the sum of capacitors is equal to the sum of capacitances of individual capacitors.capacitances of individual capacitors.

C = CC = C1 1 + C+ C22 + C + C33

( where, C = resultant capacitance ( where, C = resultant capacitance

andand

C1,C2,C3 = capacitance of C1,C2,C3 = capacitance of individual capacitors)individual capacitors)

The work done in charging a capacitor is The work done in charging a capacitor is stored in the capacitor in the form of stored in the capacitor in the form of electric energy.electric energy.

The energy stored in a charged capacitor The energy stored in a charged capacitor resides inside it in the form of electric field.resides inside it in the form of electric field.

When two charged capacitors are When two charged capacitors are connected to each other, they share connected to each other, they share charges till they acquire a common charges till they acquire a common potential. On sharing charges, there is potential. On sharing charges, there is always some loss of energy . However, always some loss of energy . However, total charge of system remains conserved. total charge of system remains conserved.

Energy stored in a charged capacitor is Energy stored in a charged capacitor is given by given by

U = ½ qV U = ½ qV

((where, U = energy stored in the where, U = energy stored in the capacitor,capacitor,

q = charge on the plate of q = charge on the plate of capacitor andcapacitor and

V = potential of capacitor )V = potential of capacitor )

Definition of dielectricsDefinition of dielectricsTypes of dielectricsTypes of dielectricsPolarisationPolarisationDielectric constantDielectric constantDielectric strengthDielectric strength

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DIELECTRICSDIELECTRICS:: The insulators which The insulators which do not conduct electricity but on do not conduct electricity but on applying electric field, induced applying electric field, induced charges are produced on its faces. charges are produced on its faces. Such an insulator is called Such an insulator is called dielectric. The valence electrons in dielectric. The valence electrons in atoms of a dielectric are tightly atoms of a dielectric are tightly bound to their nuclei and ordinarily bound to their nuclei and ordinarily cannot detach themselves. cannot detach themselves.

Types of dielectricsTypes of dielectricsNon - polar dielectricsNon - polar dielectricsPolar dielectricsPolar dielectrics

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A dielectric, in A dielectric, in the atoms or the atoms or molecules of which, molecules of which, the centers of the centers of gravity of positive gravity of positive or negative charge or negative charge coincide, is called a coincide, is called a non – polar non – polar dielectric. dielectric.

NON–POLAR NON–POLAR DIELECTRICDIELECTRIC

A dielectric, in A dielectric, in the atoms or the atoms or molecules of which, molecules of which, the centers of gravity the centers of gravity of positive or of positive or negative charge do negative charge do not coincide, is called not coincide, is called a polar dielectric. a polar dielectric.

POLAR POLAR

DIELECTRICDIELECTRIC

The The stretchingstretching

of dielectric atoms of dielectric atoms due to displacement due to displacement of charges in the of charges in the atoms under the atoms under the action of applied action of applied electric field is electric field is called poarisation. called poarisation.

POLARISATIOPOLARISATIONN

The ratio of the strength of the The ratio of the strength of the applied electric field to the strength of the applied electric field to the strength of the reduced value of the electric field on placing reduced value of the electric field on placing the dielectric between the plates of the the dielectric between the plates of the capacitor is called the dielectric constant of capacitor is called the dielectric constant of the dielectric medium.the dielectric medium.

It is also known as relative or It is also known as relative or specific induced capacity and is denoted by K specific induced capacity and is denoted by K or Eor E

rr.. Therefore, dielectric medium constant of Therefore, dielectric medium constant of

a dielectric medium is given by a dielectric medium is given by

K = EK = E00/E ( K > 1 )/E ( K > 1 )

The dielectric strength The dielectric strength of a dielectric is defined as the of a dielectric is defined as the maximum value of electric field ( or maximum value of electric field ( or potential gradient ) that can be applied potential gradient ) that can be applied to the dielectric without its electric to the dielectric without its electric break down.break down.

The unit of dielectric strength is The unit of dielectric strength is same as that of electric field i.e. Vmsame as that of electric field i.e. Vm-1-1. . However the practical unit of dielectric However the practical unit of dielectric strength is kVmmstrength is kVmm-1-1. .