SOLUTION-HCVERMA/EL.FIELD/CH.29

SOLUTION.... EL.FIELD.& POTENTIAL...H.C.VERMA

1.8.7 ELECTRIC LINE OF FORCES

 Graphical visualization of electric field in given region is done by electric lines of forces. Electric lines of force is such type of imaginary curve in any given electric field, tangent on which indicates the direction of net electric field.
PROPERTIES OF ELECTRIC FIELD LINES=
1.It starts from positive point charge and moves radially outward.They end at infinity.
2.Field lines produced due to negative charge start from infinity and directed towards the negative charge.
3.Field lines start from positive charge and end towards negative charge.
4.These  lines do not form closed loop.[*field lines in induced electric field may form closed loop,since such field is non-conservative.]
5.Field lines have the tendency of contraction along the length. This indicate that opposite charges have attraction.
6. Properties of lateral expansion indicates that like charges repel each other.

1.9 ELECTRIC FIELD LINES

1.8.2 PHYSICAL SIGNIFICANCE OF ELECTRIC FIELD

Electric field at a point in  the space around a system of charges tells us the force a unit positive
test charge would experience if placed at that point (without disturbing the system). Electric field is a characteristic of the system of charges and is independent of the test charge that we place at a point to determine the field. The term field in physics generally refers to a quantity that is defined at every point in space and may vary from point to point. Electric field is a vector field, since force is a vector quantity. consider the force between two distant charges q1, q2 in accelerated motion. Now the greatest speed with which a signal or information can go from one point to another is c, the speed of light. Thus, the effect of any motion of q1 on q2 can not arise instantaneously. There will be some time delay between the effect (force on q ) and the cause (motion of q ). arise instantaneously. There will be some time delay between the effect (force on q2) and the cause (motion of q1). The accelerated motion of charge q1 produces electromagnetic waves, which then propagate with the speed c, reach q2 and cause a force on q2.  Thus, even though electric and magnetic fields can be detected only by their effects (forces) on charges, they are regarded as physical entities, not merely mathematical constructs.

1.8.1 ELECTRIC FIELD DUE TO SYSTEMS OF CHARGES

Consider a system of charges q₁, q₂, ………..q_n placed at distances r₁, r₂….r_n with respect to some origin. Then the electric field intensity due to all these charges at a point is found out using the Principle of superposition. Let  intensity due to the number of charges q₁, q₂, ………..q_n. Then the resultant electric intensity  at that point due to these charges is given by the superposition theorem.

Electric field intensity due to the n^th charge is

Magnitude of the electric field intensity is given by the equation:

1.8 ELECTRIC FIELD

DEFINITION OF ELECTRIC FIELD           
"The electric field due to a charge Q at a point in space may be defined as the force that a unit positive charge would experience if placed

at that point."

The charge Q, which is producing the electric field, is called a source charge and the charge q, which tests the effect of a source charge, is called a test charge
 The direction of the field is taken to be the direction of the force it would exert on a positive test charge. The electric field is radially outward from a positive charge and radially in toward a negative point charge.




ELECTRIC FIELD DUE TO POINT CHARGE

The electric field of a point charge can be obtained from Coulomb's law: The electric field is radially outward from the point charge in all directions. The circles represent spherical equipotential surfaces.

The electric field from any number of point charges can be obtained from a vector sum of the individual fields. A positive number is taken to be an outward field; the field of a negative charge is toward it.

1.4 CHARGING BY CONTACT/ INDUCTION

When we touch a pith ball with an electrified plastic rod, some of the negative charges on the rod are transferred to the pith ball and it also gets charged. Thus the pith ball is charged by contact.
Let take  two metal spheres A and B in contact with each other and standing on an insulating stand.
When we bring a positively charged rod near one of the spheres{A}, the free electrons in the spheres are attracted towards the rod. This leaves an excess of positive charge on the rear surface of sphere B. Both kinds of charges are bound in the metal spheres and cannot escape. They, therefore, reside on the surfaces,  The left surface of sphere A, has an excess of negative charge and the right surface of sphere B, has an excess of positive charge. However, not all of the electrons in the spheres have accumulated on the left surface of A. As the negative charge starts building up at the left surface of A, other electrons are repelled by these. In a short time, equilibrium is reached under the action of force of attraction of the rod and the force of repulsion due to the accumulated charges. The process is called induction of charge  The accumulated charges remain on the surface,till the glass rod is held near the sphere. If the rod is removed, the charges are not acted by any outside force and they redistribute to their original neutral state.In this process, the metal spheres will each be equal and oppositely charged. This is charging by induction. The positively charged glass rod does not lose any of its charge, contrary to the process of charging by contact.

CHARGING BY INDUCTION



Example 1  How can you charge a metal sphere positively without touching it?
Ans=use charging by induction law.

Example 2 If 109 electrons move out of a body to another body every second, how much time is required to get a total charge of 1 C on the other body?
Ans= use [q=]n.e=i.t
              n=i.t/e

Example 3 How much positive and negative charge is there in a cup of water?
ans=use q=ne and assume mass of one cup water='m' gram
     no of molecules of water in a cup=m/18 *6.02*10P[-23]
   here P denotes power


 

1.7 PRINCIPLE OF SUPERPOSITION [FORCES BETWEEN MULTIPLE CHARGES]

force on any charge due to a number of other charges is the vector sum of all the forces on that charge due to the other charges, taken one at a time. The individual forces are unaffected due to the presence of other charges. This is termed as the principle of superposition.

consider a system of three charges q1, q2 and q3,

1.6 COULOMB'S LAW

Any two charged objects will create a force on each other.   Opposite charges will produce an attractive force while similar charges will produce a repulsive force.  The greater the charges, the greater the force.  The greater the distance between them, the smaller the force.  For two spherically shaped charges the formula would look like:

F  the force on each charge, + indicates repulsion, - indicates attraction k the electrostatic constant   q1 the quantity of charge 1 measured in coulombs q2 the quantity of charge 2 measured in coulombs r the radius of separation from center of one charge to the center of the other.

The forces are force pairs of each other so they will always be equal in size and opposite in direction. 

COULOMB'S LAW IN VECTOR FORMSuppose that two charges,  and , are located at position vectors  and . The electrical force acting on the second charge is written 

Consider  charges,  though , which are located at position vectors  through . Electrical forces obey what is known as the principle of superposition. The electrical force acting on a test charge  at position vector  is simply the vector sum of all of the Coulomb law forces from each of the  charges taken in isolation. In other words, the electrical force exerted by the th charge (say) on the test charge is the same as if all the other charges were not there. Thus, the force acting on the test charge is given by 

Example 4 Coulomb’s law for electrostatic force between two point charges and Newton’s law for gravitational force between two stationary point masses, both have inverse-square dependence on
the distance between the charges/masses. (a) Compare the strength of these forces by determining the ratio of their magnitudes (i) for an electron and a proton and (ii) for two protons. (b) Estimate the accelerations of electron and proton due to the electrical force of their mutual attraction .

ANS= USE F[e]/F[g]

1.3.1 UNIFICATION OF ELECTRICITY AND MAGNETISM

Electricity deals with charges on bodies, batteries, lightning, etc., while magnetism
described interactions of magnets, iron filings, etc.In 1820  Oersted observed that a compass needle is deflected by passing an electric current .
 Ampere and Faraday stated that charges in motion produce magnetic fields and moving magnets

generate electricity. Maxwell's equation and Lorentz theory proved the unification of these areas.
Maxwell put forth four equations that play the same role in classical electromagnetism as Newton’s equations of motion and gravitation law play in mechanics. He also argued that light is electromagnetic in nature and its speed can be found by making purely electric and magnetic measurements. He claimed that the science of optics is intimately related to that of electricity and magnetism.

1.3.1 CONDUCTORS/INSULATORS

Those  substances which allow electricity to pass through them easily are called conductors. They have electric charges (electrons) that are comparatively free to move inside the material. Metals, human and animal bodies and earth are conductors.When some charge is transferred to a conductor, it readily gets distributed over the entire surface of the conductor.




Most of the non-metals like glass, porcelain, plastic, nylon, wood offer high resistance to the passage of
electricity through them. They are called insulators.if some charge is put on an insulator, it stays at the same place.


This property of the materials tells you why a nylon or plastic comb gets electrified on combing dry hair or on rubbing, but a metal article like spoon does not. The charges on metal leak through our body to the
ground as both are conductors of electricity.

EARTHING =  When we bring a charged body in contact with the earth, all the excess charge on the body disappears by causing a momentary current to pass to the ground through the connecting conductor (such as our body). This process of sharing the charges with the earth is called grounding or earthing. Earthing provides a safety measure for electrical circuits and appliances. A thick metal plate is buried deep into the earth
and thick wires are drawn from this plate; these are used in buildings for the purpose of earthing near the mains supply.

1.2.1 GOLD LEAF ELECTROSCOPE

gold-leaf electroscope is the simple apparatus to detect charge on the body.
 construction= It consists of a vertical metal rod housed in a box, with two thin gold leaves attached to its bottom end.
working= When a charged object touches the metal knob at the top of the rod, charge flows on to the leaves and they diverge. The degree of divergence is an indicator of the amount of charge.The white paper strips is used to explain the working of the apparatus. We fold the strips into half so that we make a mark of fold.We  open the strip and iron it lightly with the mountain fold up.We hold the strip by pinching it at the fold.We notice that the two halves move apart.This shows that the strip has acquired charge on ironing. When we fold it into half, both the halves have the same charge. Hence they repel each other. The same effect is seen in the leaf electroscope.
 On charging the curtain rod by touching the ball end with an electrified body, charge is transferred to the curtain rod and the attached aluminium foil. Both the halves of the foil get similar charge and therefore repel each other. The divergence in the leaves depends on the amount of charge on them.
 Why material bodies acquire charge.?
We know that all matter is made up of atoms and/or molecules. Although normally the materials are electrically neutral, they do contain charges; but their charges are exactly balanced. Forces that hold the
molecules together, forces that hold atoms together in a solid, the adhesive force of glue, forces associated with surface tension, all are basically electrical in nature, arising from the forces between charged particles.
.To electrify a neutral body, we need to add or remove one kind of charge. When we say that a body is charged, we always refer to this excess charge or deficit of charge. In solids, some of the electrons, being
less tightly bound in the atom, are the charges which are transferred from one body to the other. A body can thus be charged positively by losing some of its electrons.
When we rub a glass rod with silk, some of the electrons from the rod are transferred to the silk cloth. Thus the rod gets positively charged and the silk gets negatively charged. No new charge is created in the process of rubbing. Also the number of electrons, that are transferred, is a very small fraction of the total number of electrons in the material body. Also only the less tightly bound electrons in a material body can be transferred from it to another by rubbing.

1.2 ELECTRIC CHARGE

The name electricity is coined from the Greek word elektron meaning amberIt was observed that if two glass rods  rubbed with wool or silk cloth are brought close to each other, they repel each other. However, the glass rod and wool attracted each other. Similarly, two plastic rods rubbed with cat’s fur repelled each other  but attracted the fur.It was concluded, after many careful studies that there were only two kinds of an entity which is called the electric charge The experiments on pith balls suggested that there are two kinds of electrification and we find that (i) like charges repel and (ii) unlike charges attract each other. The experiments also demonstrated that the charges are transferred from the rods to the pith balls on contact. It is said that the pith balls are electrified or are charged by contact. The property which differentiates the two kinds of charges is called the polarity of charge.the charges were named as positive and negative by the American scientist Benjamin Franklin.
FACTS
1.Charge is a derived scalar quantity, its dimensional formula is [AT].
2.Quantization of charge = it is found that charge on any body is always equal to integral multiple of charge of one electron . Charge can not be divided in random manner but can be divided in such a manner that both parts after division must be an integral multiple of elementary charge. This property of charge is called quantization of charge. q=n.e  here n=[+/-]1,2,3,4......[according to recent studies,protons,neutrons are also made of particles called as 'QUIARKS' having charges of [+/-]1/2e , [+/-]2/3e]
3. Conservation of charge=  For a given system the total charge is constant. let us take the the example of  a system of  a glass rod and silk.for this system total charge is constant,even if we rub them.Here glass rod becomes positively charge and silk negatively charged .Electrons from glass rod transferred to silk.This shows that charge can neither be created nor destroyed .it can only be transferred .
4.Unit of charge=
S.I unit =coulomb [C],   1C=6.25 × 10P[-25]
5. charge is always associated with mass. without mass charge does not exist.Partcles having zero rest mass are always chargeless.

STATIC ELECTRICITY

1.1 INTRODUCTION

 We experience a sensation of an electric   shock either while opening the door of a car or holding the iron bar of a bus after sliding from our seat. The reason for these experiences is discharge of electric charges through our body, which were accumulated due to rubbing of insulating surfaces.this is due to generation of static electricity.Static means any thing that does not move or change with time. Electrostatics deals with the study of forces, fields and potentials arising from static charges.