LECTURE 1 : CLASS XII: PHYSICS : ELECTRIC CHARGE & FIELD

CLASS XII   |    PHYSICS    |    ELECTRIC CHARGE

      Notes prepared by Subhankar Karmakar

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ELECTRIC CHARGE

Electric charge is an intrinsic property of elementary particles of matter which gives rise to electric force between various objects.

• Electric charge is a scalar quantity.
• SI unit of electric charge is coulomb (C).
• There are two types of charges- a. Positive charge and b. Negative charge.
• A proton has a positive charge (+e) and an electron has a negative charge (-e).
• Magnitude of charge of a proton and an electron are same.
• Charge of a proton = + 1.6 x 10⁻¹⁹ C
• Charge of an electron = - 1.6 x 10⁻¹⁹ C

POLARITY OF CHARGE

• The property which distinguishes the two kinds of charges is called the polarity of charge.

FUNDAMENTAL LAW OF ELECTROSTATICS: 

• Like charges repel and unlike charges attract each other.

• The charge developed on a glass rod when rubbed with silk is called positive charge.
• The charge developed on a plastic rod rubbed with wool is called negative charge. 

CONDUCTORS AND INSULATORS

• Conductors: The substances through which electric charges can flow easily are called conductors. 
• Insulators: the substances through which electric charges cannot flow easily are called insulators.
• When some charge is transferred to a conductor, it really gets distributed over his entire surface. 
• If some charge is put on an insulator, It stays at same place. 
• The process in which a body shares its charges with the earth is called grounding or earthing.

ELECTROSTATIC INDUCTION

• It is the phenomenon of temporary electrification of a conductor in which opposite charges appear at its closure and and similar charges appear at its further and in the presence of a nearby charged body. 
• When two conductors one or both are charged are in contact with each other total charge is divided into two equal parts. 
• Suppose a conductor A has charge Q and another conductor B has charged q and they are connected with each other, then each of them will have a charge equal to (Q + q)/2.
• Suppose a conductor A has charge Q and another uncharged conductor B are connected with each other, then each of them will have a charge equal to (Q/2).

CHARGING OF TWO SPHERES BY INDUCTION

Steps for charging of two spheres by induction.

1. We hold the two metal spheres on insulating stands and place them in contact.
2. We bring a positively charged glass rod near the left sphere. The left sphere then becomes negatively charged and the right sphere becomes positively charged.
3. We separate the spheres and they now have opposite charges. 
4. We remove the glass rod. The charges on the spheres get redistributed. Positive and negative charges now face each other. 
5. When the spheres are separated quite apart, the charges on them get uniformly distributed. 

CHARGING OF A SPHERE BY INDUCTION

Steps for charging of a sphere by induction

1. We take a metal sphere on an insulating stand and keep a negatively charged plastic rod near it. The near end of the sphere becomes positively charged and far end of the sphere becomes negatively charged.
2. Far end of the sphere is connected to the ground by a connecting wire to the ground. 
3. When the sphere is disconnected from the ground, the positive charge remain in the near end. 
4. When the plastic rod is removed, the positive charge is uniformly distributed on the sphere. 

BASIC PROPERTIES OF CHARGE:

• There are three basic properties of charge. They are 1. Additivity, 2. Quantization and 3. Conservation of Charge. 
• Additivity: Additivity of electric charge means that the total charge of a system is the algebraic sum of all the individual charges located at different points inside the system.
• Quantisation: The quantization of electric charge means that the total charge (q) of a body is always an integral multiple of a basic quantum of charge (e).

∴ q = ne, where n = ±1, ±2, ±3, ±4,.........

• Conservation: The laws of conservation of charge states that 
• The total charge of an isolated system remains constant. 
• The electric charges can neither be created nor destroyed, they can only be transferred from one body to another body. 

COULOMB'S LAW OF ELECTRIC FORCE:

Coulomb's law states that the force of attraction or repulsion between two stationary point charges is

1. Directly proportional to the product of the magnitude of the two charges.
2. Inversely proportional to the square of the distance between them and the force acts along the line joining the two charges. 

q₁ ⁕--------------- r ------------------⁕ q₂

If two point charges q₁ and q₂ are separated by a distance r, then the force F of attraction or repulsion between them is such that

 F ∝ q₁q₂  and  F ∝ 1 /r²

F = k q₁q₂/r²

[ Electrostatic force constant (k) ]

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

The value of k depends on the nature of the medium between the two charges and the system of units used to represent the physical quantities. 

For the two charges located in free space and in SI units, 

 k = 1/(4πεₒ) = 9 x 10⁹ Nm²/C²

Where εₒ is called permittivity of free space. 

εₒ =  8.85 x 10⁻² C² N⁻¹m⁻²

Dimension of εₒ = [M⁻¹L⁻³T⁻⁴A²]

UNITS OF CHARGE

1. The SI unit of charge is Coulomb and denoted by C. 

2. CGS unit of Charge is two types

(i) in electrostatic CGS unit: statcoulomb or e.s.u. 

1 C = 3 x 10⁹ e.s.u. of charge. 

(ii) in electromagnetic CGS unit: abcoulomb or e.m.u. of charge.

1 C = 0.1 abcoulomb or e.m.u. of charge.

COULOMB'S LAW IN VECTOR FORM

RELATIVE PERMITTIVITY AND DIELECTRIC CONSTANT 

Permittivity

Permittivity is a property of a medium which determines the electric force between two charges situated in that medium. It is denoted by ε. Permittivity of vacuum or free space is minimum and it is denoted by εₒ. Permittivity of other medium are greater than εₒ. 

Relative Permittivity

The ratio (ε/εₒ) of the permittivity (ε) of a medium to the permittivity (εₒ) of free space is called relative permittivity (εᵣ ) of the given medium. 

Dielectric Constant (κ) 

Dielectric constant is defined as the ratio of the force between two charges placed some distance apart in free space to the force between the same two charges placed at same distance apart but in another medium. It is equal to relative permittivity. κ = εₒ. 

Dielctric constant for air = 1.00054

Dielctric constant for water = 80.

SUPERPOSITION OF ELECTROSTATIC FORCES

The principle of superposition states that when a number of charges are interacting, the total force on a given charge is the vector sum of the forces exerted on it due to all other charges. The force between two charges is not affected by the presence othe other charges.