Electric Charge - Physics Notes -Class 10

INTRODUCTION

Electricity can be used for heating , lighting , running motors and a large number of other purposes . Many theories about electricity were developed through experiments and by observation of its behaviour . The only theory that has survived over the years to explain the nature of electricity is the modern electron theory of matter . This theory has been the result of research work conducted by scientists like Sir William Crooks , J.J. Thomson , Robert A. Millikan , Sir Earnest Rutherford and Neils Bohr . In this chapter , we shall deal with some aspects of static electricity i.e. electricity at rest .

MODERN ELECTRON THEORY

* An atom consists of a central part called nucleus. The nucleus contains protons and neutrons . A proton is a positively charged particle while a neutron has no charge . Therefore , the nucleus of an atom bears a positive charge .

* Around the nucleus  there are a number of electrons revolving in different paths or orbits  called extra – nucleus .

* An electron is a negatively charged particle having negative charge equal to the magnitude of  charge on 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.

* Electrons are very mobile and can be easily removed . However , protons are held very powerfully in the nucleus and cannot be removed.

 

NATURE OF ELECTRICITY

* Matter is electrical in nature i.e. matter contains particles of electricity viz . , protons and electrons .

 ( i ) If the number of protons is equal to the number of electrons in a body , the resultant charge is zero and the body will be electrically neutral .

 ( ii ) If from a neutral body , some  electrons are removed , the protons outnumber the electrons . Hence, the body attains a positive charge . Hence , a positively charged body has deficit of electrons from the normal due share .

( iii ) If a neutral gain electrons , then electrons outnumber the protons . As a result , the body acquires a negative charge . Hence , a negatively charged body has an excess of electrons from the normal due share

 

Charge :

Physical property of matter which determine amount of excess or deficit of electrons in body from normal is called charge.

 * S.I unit of electric charge is Coulomb ( C ).

TYPES OF ELECTRIC CHARGES

* When a body has deficiency or excess of electrons from normal due share , then body  is said to be charged or electrified .

* Depending upon whether electrons are removed or added to a body , there are two types of charges .

( i ) Positive charge

( ii ) Negative charge

e.g-

* If a glass rod is rubbed with silk , some electrons pass from glass rod to silk . As a result , the glass rod becomes positively charged and silk attains an equal negative charge .

* The mass of negatively charged silk will increase and that of glass rod will decrease . It is because silk has gained electrons while glass rod has lost electrons .

Q- Define +1 coulomb .

Ans- 

* When two equal positive charges are kept at 1 m distance and they exert 9 x 10⁹  N force to each other then amount of charge will be +1 C each.     Or

* If a body losses  6.25 x 1025  electrons from normal. Then amount of charge on body will be  +1 C.

 

BASIC PROPERTIES OF ELECTRIC CHARGE

 * Like charges repel each other and unlike charges attract each other .

 * Electric charge is a scalar quantity i.e it has magnitude only and no direction

  * Electric charge has additive nature .

  * Electric charge is a quantized quantity i.e , electric charge on a body has discrete ( not continuous ) values .

 *  Electric charge is a conserved quantity i.e. , in an isolated system , total electric charge remains the same .

 

ADDITIVE NATURE OF ELECTRIC CHARGE

*  The total electric charge on a body ( or system ) is equal to the algebraic sum of all the individual electric charges located at different parts of the body ( or system ) .  This is called additive property of electric charge

For example,  

*  if a body ( or system ) contains four charges + 2µC , -3µC , + 4μC and -5μC , then total charge q on the body ( or system ) is

 q = ( + 2µC ) + ( -3μC ) + ( + 4µC ) + ( - 5µC ) = 2μC 3μC + 4µC - 5μC = -2μC

 

QUANTIZATION OF ELECTRIC CHARGE

* charge on a body can only be q = ± ne where n = 1 , 2 , 3 , 4  etc.

and    e = 1.6 x10^-19   C

 

CONSERVATION OF ELECTRIC CHARGE

 The total electric charge of an isolated system always remains constant .

For example,  

(i)   When glass rod is rubbed with silk , glass rod attains positive charge while silk acquires equal negative charge . Although positive and negative charges have been developed , the net charge of the system is zero , i.e. , the same as was before rubbing .

 ( ii ) Another example of conservation of electric charge is found in the radioactive decay

 

ELECTROSTATICS

*  The word ' electrostatic ' means electricity at rest .

 The branch of physics which deals with charges at rest is called electrostatics

e.g.-

*  When a glass rod is rubbed with silk and then separated , the former becomes positively charged and the latter attains equal negative charge . Since glass rod and silk are separated by an insulating medium ( i.e. , air ) , they retain the charges . In other words , the charges on them are static or stationary .

 

IMPORTANCE OF ELECTROSTATICS

A few important applications of electrostatics are given below :

( i ) Electrostatic generators can produce voltages as high as 10⁶  volts . Such high volt ages are required for X - ray work and nuclear bombardment .

( ii ) We use principles of electrostatics for spray of paints , powder , etc.

( iii ) The principles of electrostatics are used to prevent pollution .

( iv ) The problems of preventing sparks and breakdown of insulators in high voltage engineering are essentially electrostatic .

( v ) The development of lightning rod and capacitor are the outcomes of electrostatics

 

CONDUCTORS AND INSULATORS

The substances are divided into two classes on the basis of their ability to conduct electric charges :

( i ) Conductors    ( ii ) Insulators

( i ) Conductors  

*  Those substances through which electric charges can flow easily are called conductors e.g .. silver , copper , aluminium  etc.

*  In a metallic conductor , there are a large number of free electrons which act as charge carriers . However , in a liquid conductor , both positive and negative ions are the charge carriers .

 ( ii ) Insulators

*  Those substances through which electric charges cannot flow are called insulators .  e.g .. glass , rubber , mica etc.

*  When such materials are charged by rubbing , only the area that is rubbed becomes charged and there is no tendency of the charge to move into other regions of the substance .

 

FRICTIONAL ELECTRICITY

*  The electrostatic charges developed on insulating bodies when they are rubbed against each other is called frictional electricity .

e.g.   

* when glass rod is rubbed against silk cloth , the electricity developed is the frictional electricity .

 * When a charge is placed on an insulator it stays in the region in which it has been placed . On the other hand , a charge placed on a metal is quickly redistributed over the surface of the metal .

 

METHODS OF CHARGING A CONDUCTOR

An uncharged conductor can be charged by the following two methods :

( i ) By conduction ( ii ) By induction

( i ) By conduction

 * In this method , a charged body A is brought in contact with the uncharged conductor B.

 * Conductor A is provided with an insulating handle so that its charge does not escape to the ground through our body . For the same reason , the conductor B is kept on the insulating stand .

  * When the positively charged conductor A provided with insulating handle is touched with uncharged conductor B  , free electrons from conductor B move to conductor A. As a result , there occurs a deficit of electrons in conductor B and it becomes positively charged .

*  If the conductor A is negatively charged , the conductor B will also get negatively charged .

 

( ii ) By Induction .

*  In this method , a charged insulating body is brought close to the uncharged conductor but does not touch it .

*  Negatively charged plastic rod ( provided with insulating handle ) kept near an uncharged metal sphere .

 * The free electrons of the sphere near the rod are repelled to the farther end . As a result , the region of the sphere near the rod becomes positively charged and the farthest end of sphere becomes equally negatively charged .

*   If now the sphere is connected to the ground through a wire , its free electrons at the farther end flow to the ground .

  * On removing the wire to the ground  , the positive charge at the near end of sphere remains held there due to the attractive force of external negative charge .

  * Finally , when the plastic rod is removed, the positive charge spreads uniformly on the sphere . Thus , the sphere is positively charged by induction .

 

 COMPARISON OF ELECTRIC CHARGE AND MASS

ELECTRIC CHARGE:

1 . Electric charge may be positive , negative or zero .

2. Electric charge is quantized .

3 . Electric Charge on a body does not depend on its speed .

4 . Electric charge is always conserved .

5 Force between two electric charges may be attractive or repulsive depending upon the kind of charges .

6. Electric forces between different charges may cancel out .

MASS :

1. Mass of a body is always a positive quantity .

2. Quantization of mass is not yet established .

3. The mass ( m ) of a body increases with the increase in speed of the body .

4. Mass is not conserved because it can be converted into energy ( E = mc² ) and vice - versa .

5. The gravitational force between two masses is always attractive .

6. Gravitational forces between different masses never cancel out .

COULOMB'S LAW OF ELECTRICAL FORCE

According to this law , the electrostatic force between two point charges is

(i) Directly proportional to the product of their magnitudes .

      F  ∝  q_{1 .} q₂

(ii) Inversely proportional to the square of distance between their centres .

     F  ∝ 1 / r²

     i.e,      F  ∝  q_{1 .} q₂  /  r²

     or,       F = k q_{1 .} q₂  /  r²

* Where k is a constant of proportionality and called electrostatic force constant .

* The value of k depends on the nature of medium between the two charges and the system of units used .

* When the charges are situated in free space ( air / vacuum ) , then in SI units , the value of k is  9x10 ⁹  Nm² C ^{- 2}

* This force will be repulsive or attractive depending upon whether the charges are like or unlike charges .

* The force always acts along the line joining the centres of the two charges .

 

DEFINITION OF  1C FROM COULOMB'S  LAW

* If two similar charges are kept at 1 m distance and they exert 9 x 10⁹ N force on each other , then magnitude of charge is 1 C  each.

 

ABSOLUTE PERMITTIVITY

* Permittivity is the property of a medium that  affects the magnitude of force between two point charges .

* Air or vacuum has a minimum value of permittivity .

* The absolute ( or actual ) permittivity of air or vacuum is ε₀ =  8.854 x 10 ^-12  C²N'm² . The absolute permittivity ε of all other insulating materials is greater than ε₀.

Relative Permittivity Or Dielectric Constant

* The ratio ε / ε₀ , is called relative permittivity of the material and is denoted by K ( or ε_r , ) .

* Relative permittivity ( or dielectric constant ) of a medium may be defined as the ratio of force between two charges separated by a certain distance in air ( or vacuum ) to the force between the same charges separated by the same distance in the medium .

* Relative permittivity of medium is also called dielectric constant .

( i ) For air or vacuum , K = ε₀ / ε₀ = 1

 

THE SUPERPOSITION PRINCIPLE

* When a number of charges are present , the total force on a given charge is equal to the vector sum of the forces due to the remaining other charges on the given charge .

 

Electric Charge Questions -

1.  Is a charge of 4.5 x 10^-19 C  possible ?

Ans:  Not Possible

 

2.  A body has a charge of +3.2 x 10^-7 C . Calculate the less number of electrons as compared to neutral state .

Ans:   2 x  10¹²

 

3. A glass rod is rubbed with a silk cloth . The glass rod acquires a charge of + 19.2 x 10 ^-19  C.

( i ) Find the number of electrons lost by glass rod .  

 Ans : 12

( ii ) Find the negative charge acquired by silk .    

 Ans : -19.2 x 10^-19  C

( iii ) Is there transfer of mass from glass to silk ?

Ans :  Yes

 

4. Calculate the number of electrons in 100 g of water .

Ans: 3.35 x 10²⁵ 

 

5. If a body gives out 10 ⁹  electrons every second , how much time is required to get a total charge of 1C  from it ?

Ans: 198  Years

 

6. How many electrons will have a total charge of 1 C ?

Ans :  6.25 x  10¹⁸  electrons

 

7. Calculate the charge on ₂₆F⁵⁶ nucleus . Given charge on proton  = 1.6 × 10^-19 C.   

Ans:    + 4.16 x 10^-18 C 

 

8. Calculate the total positive , or negative charge on a 3.11 g copper penny . Given Avogadro number = 6.02 x 10²³ and atomic number of copper = 29 and atomic mass of copper = 63.5 .

Ans:  1.37 x 10⁵  C

 

9. How many electrons must be removed from a piece of metal to give it a positive charge of 1 x 10^-7  C  ?

Ans:  6.25 x 10¹¹ 

 

10. Calculate the charge on an alpha particle . Given charge on a proton =  +1.6 x 10^-19C .

Ans:    + 3.2 x 10^-19   C