1.20 Relation between Field and Potential

We have discussed the electric field and potential. Electric potential is a scalar quantity but electric field is a vector quantity. How are these quantities related to each otehr?

                To derive the relation between electric field and potential let us consider two closely spaced equipotential surfaces A and B as shown in figure with potential values V and V +dow V , where Dow V is the change in V in the direction of electric field E. Let P be a point on the surface B. dow l is the perpendicular distance of the surface A from P. Imagine that a unit positive charge is moved along this perpendicular from the surface B to surface A against the electric field. The work done in this process is |E | dow l


           We thus arrive at two important conclusions concerning the relation between electric field and potential: (i) Electric field is in the direction in which the potential decreases steepest. (ii) Its magnitude is given by the change in the magnitude of potential per unit displacement normal to the equipotential surface at the point

1.19 Equipotential Surface

We have discussed the potential due to point charge, electric dipole, etc. Now let us go through the equipotential surface and its properties.
          An equipotential surface is a surface with a constant value of potential at all points on the surface.

Properties of Equipotential Surface
       This shows that V is a constant if r is constant. Thus, equipotential surfaces of a point charge are concentric spherical surfaces centred at the charge. Now the electric field lines for a  single charge q are radical lines starting from or ending at the charge, depending on whether q is positive or negative. Clearly, the electric field at every point is normal to the equipotential surface passing through that point. Theis is true in general: for any charge configuration, electric field at any point is normal to the electric field at that point. Why should it be normal?

             If the field were not normal to the equipotential surface, it would have non-zero component along the surface. To move a unit test charge against the direction of the component of the field, work would have to be done. But this is in contradiction to the definition of an equipotential surface: there is no potential difference between any two points on the surface and no work is required to move a test charge on the surface. The electric field must, therefore, be normal to the equipotential surface at every point.
              
              Equipotential surfaces offer an alternative visual picture in addition to the picture of electric field lines around a charge configuration. For a uniform electric field E, say, along the x- axis, the equipotential surfaces are planes normal to the x-axis, ie, planes parallel to the y-z plane.

1.18 Electric Potential

Why do we define electric potential?        We have defined potential energy of a test charge q in terms of the work done on the charge q. This work is obviously proportional to q, (since the force at any point is qE, where E is the electric field at that point due to the given charge configuration). If we divide the work by the amount of charge q, the resulting quantity is independent of q. In other words, work done per unit test charge is characteristic of the electric field associated with the charge configuration. Thus work done per unit charge leads to the idea of electrostatic potential V due to a given charge configuration.

Wab/q = Vp
      
            This equation explain that the work done by an external force in bringing a unit positive charge from infinity to a point is equal to the electrostatic potential(V) at that point. Hence electro static potential at any point may be defined as the work done in bringing a unit positive charge from infinity to that point without any acceleration.


1.18 Potential due to a Point Charge
       The electric potential due to a point charge at a point depends on magnitude of charge, distance of the point and also on the surrounding medium. The equations shows that potential due to a point charge decreases with increase in distance and becomes zero at infinity

1.17 Electrostatic Potential Energy

        To get a clear idea about electrostatic potential energy, consider the field E due to a charge Q placed at the origin. Now, imagine that we bring a positive test chrge q from a point R to a point P against the repulsive force on it due to the charge Q.
         
             In this situation, work done by the external force(Fex) is the negative of the work done by the electric force, and gets fully stored in the form of potential energy of the charge q. Thus, work done by external forces in moving a charge q from R to P is

                   Wrp= Integral limit from R to P Fext.dr
                             (note here that this displacement is in an opposite sense to the electric force (E) and hence work done by electric field is negative,. This work done is against electrostatic repulsive force and gets stored as potential energy.

           At every point in electric field, a particle with charge q possesses a certain electrostatic potential energy, this work done increases its potential energy by an amount equal to potential energy difference between points R and P. Thus, potential energy difference.

       Therefore, we can define electric potential energy difference between two points as the work required to be done by an external force in moving (without accelerating) charge q from one point to another.

        We have discussed potential energy and potential energy difference, Which is more significant, potential energy or potential energy difference?
          
          Equation (2) defines potential energy difference in terms of the physically meaningful quantity work. The actual value of potential energy is not physically significant; it is only the difference of potential energy that is significant. To clarify this, let us add a constant value alfa to Up and Ur and find the difference

               This shows that, we can always add an arbitrary constant to potential energy at every point, since this will not change the potential energy difference:

                 The above argument gives a freedom in choosing the point where potential energy is zero without changing the value of potential energy difference. Potential energy at infinity is zero( We will learn this in next section). With this choice, if we take the point R at infinity, we get it.
       
             Since the point P is arbitrary, provides us with a definition of potential energy of a charge q at any point. Potential energy of charge q at a point ( in the presence of field due to any charge configuration) is the work done by the external force (equal and opposite to the electric force) in bringing the charge q from infinity to that point.

1.16 Electrostatic Potential

      In class XI, the notion of potential energy was introduced. When a body is taken from a potential energy was introduced. When a body is taken from a point to another against a force ( like spring force) the work done gets stored as potential energy of the body. When the external force is removed, the body retraces its path, gaining kinetic energy and losing an equal amount of potential enrgy. The sum of kinetic and potential enrgies is thus conserved. Forces of this kind are called conserved forces. Spring force and gravitational force are expamples of conservative forces.
             
               Coulomb force between two (stationary) charges, like the gravitational force, is also a conservative force. Thus, like the potential energy of a mass in a gravitational field, we can define electrostatic potential energy of a charge in an electrostatic field.
      
                  

1.15 Applications of Gauss's law

(a) Field due to an infinitely long straight uniformly charged wire
                To calculate the electric field, consider an infinitely long straight line of charge, having linear charge density lamda. Let P be a point at a perpendicular distance 'r' from the line of charge. To find the field at P, imagine a cylinder of radius 'r' having length 'l' with its axis as line of charge. Here, the cylinder is considered as Gaussian surface. P is a point on the GAussian surface.

                 The electric flux through the two circular faces is zero since electric field is normal to the area vector. Electric flux through the curved surface of cylinder.

                    By Gauss's theorem, total flux is equal to 1/epsilon zero times the net charge enclosed by the cylindrical surface. The direction of this field is normal to the curved surface passing normally to it.

(b) Electric Field Due to Infinite Plane Sheet of Charge
                   
                     Consider a plane  sheet of charge of surface density sigma. Gaussian surface which is a pillbox of area of cross section A as shown. Electric flux through the curved surface of the pill box will be zero, because electric field and area vector are normal to each other.

                       If sigma is positive E is directed normally out of the plate and if sigma is negative E is directed normally in to the plate.

1.14 Continuous Charge Distribution

       We have so far dealt with charge configurations involving discrete charges q1,12,....,1n. One reason why we restricted to discrete charges is that the mathematical treatment is simpler and does not involve calculus. For many purposes, however, it is impractical to work in terms of discrete charges and we need to work with continuous charge distributions.
       
         Consider a case that grains are spread uniformly over the floor, just one layer so that the floor is not at all seen. Now, what is the total number of grains? It is a laborious task to count one by one. So what can we do? Let us consider a unit area and count the number of grains in that area. Multiply this number by the total area and we can get the total number of grains. The number of grains per unit area can be called as surface grain density.
        
           Similarly, when charges are distributed over a finite space, it is useful to consider the density of charge. It is used in three different ways.

            i. Linear Charge Density
 (1) It is the charge per unit length. If Q charges distributed uniformly over a length 'l' then

                                lamda = Q/l

            ii. Surface Charge Density:
          It is the charge per unit area. If 'Q' charge is distributed uniformly in area 'A', then surface charge density sigma = Q/A

             iii. Volume Charge Density
           It is the charge per unit volume. If 'Q'  charge is distributed uniformly in a volume V, then volume charge density row = Q/V

1.13 Gauss's Law

Gauss's law in electrostatics explains the relation between flux related to a surface and total charge enclosed by the surface. To derive the relation, consider a charge 'q' kept at the centre of a spherical surface of radius 'r'.

a) The magnitude of electric field on the surface.
b) We can consider that the spherical surface is made up of a number of small plane area each equal to 'dS'. The angle between the direction of electric field vector and area vector is zero.
c) The electric flux through such an area element ds

d) The electric flux through the entire spherical surface.


                              ie.. Total flux over a closed surface in free space is(one/epsilone) times the total charge enclosed by the surface. This is called Gauss's theorem.

                                        If there are several charges q1,q2,q3,. inside the closed surface, each will contribute to the total electric flux. Total electric flux is the summation * the 1/epsilon

         Where epsilon q is the algebraic sum of the charges within the surfaces.

Note:
 1) Since the electric lines are emerging from the charge 'q' the electric flux will not change even if the spherical surface of arbitrary shape. So an appropriate Gaussian surface is selected based on the symmetry of the problem under consideration. The examples illustrated in the coming section demonstrates the choice of Gaussian surface.

2) Now, as far as the charge is anywhere within the closed surface, the electric flux will not change. So we can say that the total flux through a closed surface is 1/epsilonzero times charge enclosed by the surface.

3) But if we keep an electric dipole within the closed surface of arbitrary shape, net flux from the closed surface is zero. The is because the electric lines emerging from positive charge ends on negative charge. Hence no net outward or inward flux, i.e, when the net charge inside the  surface is zero, the net flux through a closed surface is zero. If the charge enclosed is positive, the flux is outward and if it is negative, flux is inward.

1.12 Electric Flux

       Consider the flow of a liquid with a velocity v through a pipe of area of cross section dS. The rate of flow of liquid (V dS) represents the flux of liquid flowing across the plane. In the case of electric field, we define an alnalogous quantity and call it the electric flux.
          Flux of liquid gives rate of flow of liquid, then what does electric flux represent?
       We have discussed that the relative density of the field lines at different points indicates the relative strength of electric field at those points. Here the mathematical quantity E delta S (electric flux) gives a measure of lines passing through the area delta S.
       On which factors do E delta S (electric flux) depend?
                      Consider a small planar element of area delta S placed normal to vector.  The number of field lines crossing the area element will be smaller. The projection of the area element normal to E is deltaS cos (theta). Thus, the number of field lines crossing delta S is proportional to EdeltaS cos(theta)
                        When theta=90 degree, field lines will be parallel to plane and will not cross it at all. From the above discussion we can understand that the electric flux depend on electric field E, area A and the orientation of area with electric field.

                       From the above discussion we can understand that the electric flux depend on electric field E, area A and the orientation of area with electric field.
                      
                        If vector E is the electric field and delta vector S is an area, the electric flux may be defined as vector E. delta vector S(dot product of vector E and delta S). Area is treated as a vector. Its direction is along the normal to the plane of area.
                   
                       If this small area is a part of a large surface, then electric flux over the surface, then electric flux over the surface.


                    

1.11 Polar and Nonpolar Molecule

In many molecules, the centers of positive charges and of negative charges lie at the same point. Therefore, their dipole moment is zero. Such molecules are called non polar molecules. CO2 and CH4 are of this type.However, they can develop a dipole moment when an electric field is applied. In some molecules, the centers of negative charges and of positive charges do not coincide. Therefore they have a permanent electric dipole moment even in the absence of an electric field. Such molecules are called polar molecules. Water molecules, H2O is an example of this type.
1.11 a) Dipole in Uniform Field
  We have discussed polar molecule and non polar molecules. Consider an electric dipole of dipole moment p = 2aq kept in a uniform external electric field, inclined at an angle theta to the field direction.

                            Equal and opposite forces +qE and -qE act on the two charges. Hence the net force on the dipole is zero. But these two equal and opposite forces whose lines of action are different constitute a torque.

        torque = any one force * perpendicular distance(between the line of action of two forces)
1.11 (b) Dipole in a Non Uniform Field
   What happens if the field is not uniform? In that case, the net force will be non-zero. In addition there will, in general, be a torque on the system as before. Let us consider the simpler situations when dipole moment(p) is parallel to non uniform electric field. In this case, the net torque is zero, but theer is a net force on the dipole.

1.10 Electric Dipole

  Two equal and opposite charges separated by a very small distance constitute an electric dipole. A molecule made up of a positive and a negative ion is an example of an electric dipole.

      e.g: NaCl,HCl etc..
The product of magnitude of any one of the charges and the length of the electric dipole is called Electric dipole moment.

Vector p= q* 2* vector a

Where 'a' is half the length of dipole. It is a vector quantity, directed from negative to positive charge.

1.10 (a) Electric field at a point on the axial line of an electric dipole

 Consider an electric dipole of moment p= 2aq. Let 'S' be a point at a distance 'r' from the center of the dipole.

 The field due to an electric dipole is directed from negative charge to positive charge along the axial line.

1.10(b) Electric field due to a dipole at a point on the perpendicular bisector of the dipole(at a point of the dipole ( at a point on the equatorial line)
    
 Consider a dipole of dipole moment p= 2aq.
         Let 'S' be a point on its equatorial line at a distance 'r' form its center. The magnitudes of electric field at 'S' due to +q and -q are equal and acts as shown in figure.
         To find the resultant electric field resolve vector Ea and vector Eb.

                      Their normal components cancel each other where as their horizontal components add up to give the resultant field at 'S'.
    E= EACos(theta) + EBCos(theta) = 2 EB Cos(theta)
                                                                      (Since EA=EB)
          The direction of the field due to the dipole at a point on the equatorial line is opposite to the direction of the dipole moment.
           Electric field due to a point charge varies inversely as the second power of distance 'r' whereas the electric field due to a dipole varies inversely as the third power of distance 'r'

Note:
 If the electric field at all points in a region has the same magnitude and same direction then that electric field can be called a uniform electric field.

1.9 Electric Field due to Different Systems

          Now let us find the electric field due to different charge distributions. We shall start from electric field due to a point charge and then electric field due to a number of point charges, electric field due to a dipole and interaction between dipole and uniform field. We further discuss electric field due to symmetric charge distributions like line charge, sheet of charge and charged conduction sphere.

1.9 (a) Electric Field at a point due to a Point Charge

                     Let 'P' be a point at a distance 'r' from a point charge 'q' in air. To find the electric field at 'P', imagine a unit positive charge kept at 'P'.

        Note:
   The electric field at a point P due to a point charge is independent of the charge kept at the point P.

1.9 (b)  Electric Field at apoint due to a System of Point Charges

                Consider a system of charges q1,12, q3,.......qn. Can you find net electric field intensity at any point due to a system of charges?
                    Electric field is a vector quantity. Hence electric field at any point due to a system of charges can be found using super position principle.
                 
      Vectors Ep= E1p + E2p + E3p + ............ Enp

Electric field at a point due to a number of charges is the vector sum of electric field due to individual charges.
Note:
  1. In order to find the electric field at a point, imagine a unit positive charge kept at that point. The force acting on it will give the electric field at that point both in magnitude and direction.
2.If we keep a charge 'q' in an external electric field "E' Then the force actingo on that charge F= qE

Vectorialy F=qE
3.With a point charge as center, all along the surface of a sphere the electric field has the same magnitude (value) but directions normal to the surface of the sphere.

1.8 Electric Field

Consider a point charge Q placed in vacuum at the point O. If we place another point charge q at a point P, where OP=r, then the charge Q will exert a force on q according to Coulomb's law. We may ask the question: If the charge q is removed, then what is left at P? If there is nothing at the point P, then how does a force act when we place a charge q at P?
         
                To overcome this troublesome idea of non contact force, Michael Faraday introduced the concept of electric field.  The idea is that, surrounding every charge, there is its electric field like the light around a burning lamp. The modification made on the surrounding space by a charge or charge distribution is called it's electric field.

              When two charges q and Q are placed near to each other, each of them is situated in the field of the other. In other words, we can consider the interaction between two electric charges as the interaction between their electric fields. So if we know the electric field at a point we can calculate the electric force acting on a charge kept at that point.
         
              One of the important problems in electrostatics is to find the electric field due to different charge distributions

 Electric field Intensity
  
                   Electric field intensity at a point is defined as the force experienced by a a unit positive charge kept at that point. Electric field is a vector quantity.

           Let 'P' be a point in an electric field. To find the electric field intensity 'E' at 'P', imagine a small test charge q kept at  'P' so that it experiences a force 'F'. Then force acting on unit charge = F/q.
         By definition,  this is the electric field at P
                                E = limit q to zero (F/q)
( The test charge must be very small; otherwise it may disturb the electric field).
  Unit of electric field is newton/coulomb (N/C) or volt/meter(V/m). It's dimentional formula is MLT^-3A^-1

1.7 Coulomb's Force due to a Number of Point Charges (Super position Principle)

Electric force between two charges is given by Coulomb's law. Let us calculate the force on a charge due to several point charges in it's neighborhood.
       Consider a system of three charges q1,q2 and q3. Let r1,r2, and r3 be the position vectors of these charges from an arbitrary origin O.
          Force is a vector quantity. Hence vector law of addition can be used to find the resultant force acting on the charge q1.


        Force on q1 due to q2 is Vector F12
Simillarly,
        Force on q1 due to q3 is Vector F13

Therefore resultant force on charge q1 is
       vector F1 = vector F12 + vector F13
   
                   If we consider a system of charges q1, q2,.....qn What is the resultant force on q1 due to q2,q3,.........qn?

 Using vector law of addition , vector F1 is the summation of vector F12,F13,......F1n

 The force on one charge say q1, due ot other charges can be obtained by performing a vector addition of the forces due to other charges. This method of addition of forces is termed as principle of super position in electrostatics.
     Super position principle can be stated like this  , The force on a point charge due to  a number of point charges is equal to the vector sum of forces due to individual charges.

1.6 Coulomb's Inverse Square Law

        In activity 1, we have seen positive charge on wool and negative charge on the balloon exert force on each other. Leaves of electroscope will collapse after the charged rod is pulled back without touching the electroscope. What conclusions can be made from these observations?
        
        From these observations, we can conclude that, the force between two charged bodies increase in magnitude of charges. But force between charged bodies decrease with increase in distance between them.

       A French Physicist Charles Augustine de Coulomb found out a quantitative law about the force between two charges. According to Coulomb's law.
         Electrostatic force (F) of attraction or repulsion between two point charges 'q1' and 'q2' separated by a distance 'r' is directly proportional to the product of the charges and inversely proportional to the square of the distance between them.

        Where k is a constant of proportionality. The value of k depends on the units of F, q and r.
                      
Unit Charge or One coulomb of Charge

   How can you define unit charge?  Suppose, two unit charges are separated by a distance 1m apart in vacuum, then what will be the force of repulsion between them?

             With reference to the force experienced by unit charge, it can be defined as follows.
Unit charge is the charge which experiences a repulsive force of 9*10^9 N from an equal and similar charge, kept at a distance of 1 m in air or vacuum.
         In SI system one columb is that charge which flows through any section in one second causes 1A current.
      
           Experimentally it was found that the colomb force depends on the medium betwen the charges. In a medium, Coulomb's law differs a little
             Relative permittivity or dielectric constant of a medium is defined as the ratio of the permittivity of the medium to the permittivity of the vacuum.

  The value of dielectric constant for any material medium is greater than 1. This implies that electrostatic force between two point charges is maximum in vacuum.

             

1.5 Basic Properties of Electric Charge

From the activity 1, we have seen that there are two types of charges. Let us discuss some other properties of electric charge.
a) Unlike charges attract and like charges repel.
b) Charge is conserved

   In activity 1, we have discussed that balloon acquires negative charges when rubbed with wool. From where are these charges generated? Is any new charge created? Does this charge creation obey any conservation law?
      We have already discussed ( in activity 1), the fact that when bodies are charged by rubbing, there is transfer of electrons from one body to the other; Charges are neither created nor destroyed.
     The negative charge acquired by balloon is exactly equal to the charge lost by wool. If we take balloon and wool as a system, we can summaries the above mentioned facts as total charge on an isolated system* remains constant. This is called conservation of charge.
     Sometimes, nature creates charged particles: a neutron turns into a proton and an electron. The proton and electron thus created have equal and opposite charges and the total charge is zero before and after the creation.
     Another example is found in the fission reaction. Charge before and after fission is the same

c) Electric Charge is Quantized:
    We have discussed the transfer of charges during rubbing. What is the minimum quantity of charge transferred from one material to another material?
    
       Any physical quantity is said to be quantized if it can take only discrete values. Energy of an electron in a particular orbit and wavelength of a stationary wave produced on a stretched string are examples. Each electron/ proton carries a charge of magnitude 1.6*10^-19 C. This is the elementary or basic amount of charge. We cannot find stable charges which are fractions of these. Charge on any body is the integral multiple of electronic charge. This is called quantization of charge.

           ie, q= +or- ne where n = 1,2,3,..

        We can have bodies with charge +5e, -16e, but not 3.62e. Any amount of charge in the universe can be expressed as an integral multiple of the basic amount of charge e.
    
        The quantization of charge was first suggested by the experimental laws of electrolysis discovered by the English experimentalist Faraday. It was experimentally demonstrated by Millikan in 1912.

(d) Additivity of Charges

        What will happen if two equally and oppositely charged bodies (balloon and wool) are brought in contact?
        If a system contains two point charges q1 and q2, the total charge of the system is obtained simply by adding algebraically q1 and 12, If a  system contains n charges q1,q2,q3,....qn, then the total charge of the system is q1+q2+q3+.......+qn. Proper signs have to be used while adding the charges of a system containing five group of charges +7, +2,-8,+4 and -6, in some arbitrary unit, is(+7) +(+2)+(-8)+(-6)=-1 in the same unit.

             NOTE
         If the size of charged bodies are very small compared to distance between them, we treat them as a point charge. All the charge content of the body is assumed to be concentrated at one point in space.

1.4 Charging of a body

Rub a glass rod vigorously with silk. Bring the tip of the electroscope with glass rod as shown in figure. What do you observe? Do the leaves separate farther if you rub harder? Why do the leaves collapse after the charged rod is pulled back without touching the electroscope?
             Due to the rubbing, glass rod gets positive charge. When this positively charged glass rod is brought near the metal cap, free electrons of the copper wire are attracted towards the glass rod. Due to this attraction, electrons pile up at the near end  and the further end (leaves) become positively charged. The positive charges at the leaves produce repulsion on it. If the glass rod is taken away, the electrons re-distribute and the electroscope becomes neutral. Hence the leaves collapse.
          When a charged body is brought near a conductor, opposite charges are developed on it. This phenomenon is caled electro static induction.
               Charging by Conduction
          Touch a charged rod to  the electroscope and remove it. What do you observe? Why?
 When the charged body touches the electroscope, charge will flow to it and electroscope acquires charge similar to that of the charged body. Thus Charging a body with actual contact of another body is called charging by conduction.


             Charging by Induction

Activity 2
      Rub the glass rod vigorously with silk. Bring the glass rod near the top of electroscope as shown in figure. Then touch your finger on the top of the metal sphere.

                     What do you observe? Why don't the leaves collapse after the charged rod and finger are pulled back?
       While touching the ball of the  electroscope with finger, the negative charge of the rod will flow to the earth through your body. After removing the rod and the finger the leaves move apart, indicating that the electroscope is now positively charged due to loss of electrons.
                 Such a process in which permanent charge is imparted on a conductor by a combined action of electrostatic induction and earthing is called charging by induction.
 

1.3 Conductors and Insulators

    A metal rod held in hand and rubbed with wool will not show any sign of being charged. However, if a metal rod held with a wooden or plastic handle is rubbed, it shows signs of charging. Why? Some substances readily allow passage of electrons throught them, others do not. Those which allow electrons 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 conduction. Most of the non-metals like glass,porcelain, plastic,nylon,wood etc. Offer high resistance to the passage of electricity through them. They are called insulators. Most substances fall into one the two classes stated above.
              When charge is transferred to a conductor, it readily gets distributed over the entire surface of the conductor. In contrast, if some charge is put on an insulator, it stays at the sample place. When we bring a negatively charged body in contact with the earth, all the excess charge on the body disappears by a momentary flow of electrons to the group through the connecting conductor( such as our body).  If a positively charged body is connected to the earth, electrons flow from the earth to the body. This process of sharing the charges with the earth is called grounding or earthing. Everything provides a safety measure for electrical circuits and appliances.

1.2 Electric Charge:

The property of electrons and protons, which give rise to electric force between  them is called electric charge. By convention, the charge on an electron is taken to be negative; therefore charge on an electron is written as -e and that on a proton as +e. It is a scalar quantity. It's SI unit is coulomb(C).

                 

1.1 Frictional Electricity

Activity 1(a): The wool and balloon do not show attraction. The explanation for this observation is given below:
We know that an atom consists of a central part called nucleus and around the nucleus there are a number of electrons revolving in different orbits. The nucleus contains protons and neutrons. A proton is a positively charged particle while a neutron has no charge. Electrons are negatively charged particles. The magnitude of the charge of an electron is the same as that of a proton. Normally, the number of electrons is equal to the number of protons in an atom. Therefore, an atom is neutral as a whole: the negative charge on electrons cancelling the positive charge on protons. This leads to the conclusion that under ordinary conditions, an atom is neutral. Matter is made up of atoms. Hence a material body is electrically neutral.


            From the above explanation we can understand that wool and balloon are electrically neautral. Hence in the above activity wool and balloon do not  show any attraction or repulsion.

         In activity  1(b) the rubbed balloon and wool attract each other. The reason is that when the wool is rubbed with the balloon, friction between wool and balloon transfer loosely bound elecrons from wool to balloon. Thus wool loses electrons and gets positively charged and the balloon gains electrons and becomes negatively charged.
          
             The electricity developed on objects, when they are rubbed against each other is called frictional electricity or static electricity.

          In activity 1 (C) the balloons repel each other. This is due to the repulsion between the same type of charges developed on the balloons due to rubbing.
         From activity 1 (b) and 1 (c) we can conclude that objects which have opposite charge attract each other. Objects with similar charges repel each other.
        
          What is the meaning of a positively charged body? When one or more electrons escape from an atom , the number of electrons in that atom becomes less than the number of protons. Therefore, the net charge of the atom becomes positive. Thus a  positively charged body has deficiency of electrons in the body as compared to its neutral state and a negatively charged body has excess of electrons.