Electrostatics

ELECTROSTATICS

 The branch of physics that deals with electricity at rest is called electrostatic. The electricity can be generated due to friction and such electricity are known as frictional electricity. It is also called static electricity as the charges so developed on a body cannot move from one point to some other points.

The substance having the attracting property are said to be electrified or to possess electric charge or they are simply called charged body. Such attracting property can be acquired by rubbing many substances like fur, glass, and ebonite. 

 Fundamental of electrostatic.

1. Whenever there is imbalance in the no of protons or electron, the atoms is said to be charged.

2. If the number of protons is greater than number of electron in an atom then, the atom is said to be positively (+ve) charged and vice versa.

  Electric charge

The physical property of matter that causes it to experience a force when placed in an electromagnetic field. There are two types of charge:

•        Positive charge

•        Negative charge

The unit of charge is coulomb(C). It is denoted by 'q'. For an electron it is denoted by 'e'. 

   Properties of electric charge

1. Likes charges repeals each other and unlike charge attracts each other.

2. The magnitude of charge on a body is not affected by the speed of the body.

3. Electric charge is scalar quantity, i.e. it does not obey the laws of vector algebra. The total charge on a body is the algebraic sum of all charges distributed over different parts of it.

4. Quantization of charge: The fundamental charge associated with an electrons is called basic charge. The charge on an electron is -e. The charge in protons is +e. These are supposed to be the basic unit of electric charge.

The charge on any charged particle is the integral multiple of basic charge (e) which is called Quantization of electric charge.

The value of basic charge is taken as 1.6 × 10 ^-19 C. Therefore, Q= n e where e is the charge on an electron and n is any integer.

          

Q). Find the number of electrons in 1 coulomb charge?

Soln.

          Charge (q) = 1 C

          No of electron (n) =?

 Charge of electrons (e) = 1.6 × 10 ^-19 C

    We know

Charge (q) = n e 

Or, 1= n. 1.6 × 10 ^-19

Or, 1/(1.6 × 10 ^-19) = n

Therefore, n= 6.25× 10¹⁹

   Electrostatic Induction

The method of charging an uncharged body by bringing it near to another charged body is called Electrostatic Induction.

This process is temporary .The body is charged until it is closed to another charged body.

Induced Charges and Inducing Charges

The two kinds of charge that appears on the two end of the conductor due to induction are called inducing charge. The charge which are induced in a body closed to the inducing charge are called bound charge. They are strongly bounded by the opposite charges in the charged body.

The charge which are induced in the body far from the inducing charge are called free charge. If the conductor is connected to the earth, the free charge flows to the earth.

The charge presents in the charged body which causes other body to be charged are called the inducing charges. It is found that the either kinds of the inducing charge is equal in magnitude to the inducing charges.

    Charging a body by induction

A body can be charged by induction by the following method.

Charging a body negatively by induction

A body can be charged negatively by induction in the following ways:-

step÷1: If a positively charged glass rod is brought near a body PQ, the end P of the body acquires bound negative charge and the end Q acquires free positive charge due to induction as shown in figure (a).

          Step÷2: The body PQ is earthed with the help of metal wire as shown in figure (b). So, the free positive charge flows to earth but bound negative charge does not flows to earth.

          Step÷3: The earthing is removed but glass rod is still remains there as shown in figure(c).

          Step÷4: Finally, the positive charge glass rod is removed from the body, then the bound charge spreads all over the body and, thus the body becomes negatively charged by induction.

Charging a body positively by induction

A body can be charged positively by induction in the followings ways:-

          If a negatively charged ebonite rod is brought near a body PQ, the end P of a body acquires bound positive charge and the end Q acquires free negative charge due to induction as shown in figure (a).

          The body PQ is earthed with the help of metal wire as shown in figure (b). So, the free negative charge flows to the earth but bound positive charge does not flows to the earth.

          The earthing is removed but the ebonite rod is still remains there as shown in figure (c).

          Finally, the negatively charged ebonite rod is removed from the body PQ, then the bound positive charge spreads all over the body and thus the body becomes positive spreads all over the body and thus the body becomes positive Finally, the negatively charged ebonite rod is removed from the body PQ, then the bound positive charge spreads all over the body and thus the body becomes positively charged by induction.

                                Conductors and Insulator

Those substances which allow the electric charge to flow through it are called Conductors. Copper, brass, silver, mercury, human body, acidic water, earth etc. are the examples of conductor. Conductors can be charged by friction but the charges they acquires do not remain localized and spread over the whole surface.

Those substances which does not allow the electric charge to flow through them are called Insulators.

Glass, polythene, silk, rubber, dry air, pure water, etc. are the examples of Insulators.

Insulators can gain charged by friction but the charge cannot move to other parts of the body and remains localized.

                          Surface charge density

    The surface charge density is defined as the amount of charge per unit surface area.

    i.e.    Surface charge density = charge (q) / Surface area (A)

The unit of surface charge density is C m ^-2 coulomb per sq. meter.

 The surface density of charge depends upon the shape of conductors.

The surface charge density at all points of a spherical charge conductor is same as shown in figure (a).

       

   The surface charge density in rectangular charge body is more at the corners that at the plane. In case of conical conductor, the charge density is maximum at the apex than at other points.

                     Action of points

     The process of losing charge from the pointed body is called action of point.

A charged conical sphere contain a pointed end with less circumference, the circumference is less the surface charge density is high. As we know surface charge density is related to the action of point, the conical sphere loses charge in more amount. This is the phenomenon of action of point in a charged conical sphere.

Note: - The action of points is used in lightning conductors. Lightening conductors with sharp pointed ends are fitted at the top of a building in order to have a safe discharge of electricity generated in the atmosphere.

           The electric poles supporting the high voltage transmission lines are fitted with pointed conductors at the top. If there is any leakage of charge from the transmission lines to the poles, it is discharged through the pointed ends.

 Electrostatic Force, Field and Potential

The force that exist between any two charge particles separated by a distance id called electrostatic force. This force is attractive or repulsive in nature.

The forces between charged bodies was first experimentally measured by Coulomb in 1785. On the basis of his measurements, Coulomb enunciated a law which is known as Coulomb's law, after his name.

Coulomb's law states that “the two charges attract or repel each other with a force which is directly proportional to the product of the magnitude of the charges and inversely proportional to the square of distance between them."

  Suppose two charges Q 1 and Q 2 separated at a distance 'r' as shown in figure.

According to the Coulomb's law, the force F between the charges is

•        Directly proportional to Q1×Q2

     i.e. F∝ Q1×Q2 --------- (I)

•        Inversely proportional to square of distance between them

      i.e.  F∝1/r² ----------- (ii)

Combining these relations, we gets

                F∝ Q1×Q2/r ²

       Or, F= K Q1×Q2/r² -------- (iii)

Where K is proportionality constant. It depends upon the medium between the charges and the system of units used.

  If the charges are situated in vacuum or air, In SI unit.

           K= 1/(4πε₀ )

Where E0= permittivity of free space whose value is 8.85×10-12 C 2N -1 m -2

Therefore, F= [1/(4πε₀)]Q1×Q2/ r² -------- (IV)

This is called Coulomb's law. 

Relative permittivity (Dielectric Constant)

The ratio of permittivity of medium to the permittivity of free space is called relative permittivity.

      I.e. Relative permittivity= permittivity of medium/permittivity of free space

                  Or, ε_r = ε/ε₀

    So, ε= ε₀× ε_r

Relative permittivity is also called dielectric constant (K).

Let two charges Q1 and Q2 separated by distance 'r' are placed in medium with permittivity (E) then,

Electrostatic force F _medium = [1/4πε] (Q1×Q2/r²) --------- (I)

The same charges are placed in air keeping distance same then,

  Electrostatic force F = [1/4πε] (Q1×Q2/r²) --------- (ii)

Dividing equation (I) by (ii) we get,

F _medium / F _air =ε/ε₀ = K

 Electric Field

The space around an electric charge in which the electrostatic force of attraction or repulsion exists is called electric field.

 Electric field strength (E)

Electric field strength at a point is defined as the force experienced by a unit positive charge placed at that point.

If 'F' is the force experienced by the unit positive test charge Q₀ at a point in an electric field, the electric field intensity is given by

                                 E= F/Q₀