PHYSICS NOTES: COULOMB'S LAW PART-1

 

Electrostatics: - It is that branch of physics that deals with the charges at rest. ‘Electro’ means study of charges and ‘Static’ means at rest.

 

What is charge? Give types of charges?

Charge: - It is scalar quantity possessed by body by virtue of which the body will show attraction or repulsion on the similar charged bodies.

Types of Charges: - There are two types of Charges Positive charges and Negative charges. Like charges repel each other and unlike attract each other.


What is the cause of charging?

The cause of charging a body is the transfer of electrons from one body to another.

The body which losses electron, becomes positively charged. The body which gains electrons becomes negatively charged.

What is the effect on mass due to charging of a body?

As charging is due to the transfer of electrons. Therefore body which gains electrons becomes negatively charged and its mass increases.

Whereas the body which losses electron becomes positively charged and its mass decreases. This change in mass is negligible as mass of electrons is very small i.e 9.1x 10⁻³¹ kg




What is charging by contact?

Charging by Contact:  When a charged object is touches another object, the other object also gets charged with same polarity due to charge transfer.  This is called charge by contact.

What is charging by Induction? 

When a charged object is brought closer to another object (not touched), the original object doesn’t lose any charge and the other object gets charged as well with opposite polarity. The other extreme end of the newly charged object develops polarity same as that of the charged object. This type of charging is called charge by induction.

Properties of Electric Charge

1. Like charges repel while unlike charges attract each other. The true test of electrification is repulsion and not attraction as attraction may also take place between a charged and an uncharged body and also between two oppositely charged bodies. 

2. Charge is a scalar. ( because charge has only magnitude no direction. 
3. Charge is transferable. 
(Explanation:  When a charged body is put in contact with an uncharged body, the uncharged body becomes charged due to transfer of electrons from one body to the other. If the charged body is positive, it will draw some electrons from the uncharged body and if it is negative then it will transfer some of its excess electrons to the uncharged body) 

4. Charge is always associated with mass: Charge cannot exist without mass though mass can exist without charge. 

5. Charge is Additive. The total charge on a system   can be obtained by algebraically adding all the  charges  present on that system .

𝑞 = 𝑞1 + 𝑞2 + 𝑞3 

For a system containing n  charges , the total charge of the system can be written as, 𝑞 = 𝑞1 + 𝑞2 + 𝑞3 + … … + 𝑞𝑛     

6. Electric charge is conserved.   According to the principle of conservation of charges, the charges are neither created nor destroyed; they are only transferred from one body to the other. 



(Explanation: BEFORE RUBBING TOTAL  CHARGE ON BODY A AND B = 0     
after rubbing let 5 electrons transfer from body A to B . Then body B gets -5e charge , then Body will get +5e charge             
                
Total charge after rubbing -5e+ +5e =0) 




7 Electric Charge is quantized.   According to the principle of quantization of electric charge, all the changes on a body  are integral multiples of elementary charge( e) 
 𝑞 = 土 𝑛𝑒 Where n is an integer (zero, a positive or a negative number) and e is the basic unit of charge, that is, the charge carried by an electron or a proton. The value of e is 1.6 × 10⁻¹⁹C 

What is the cause of quantisation? The cause of quantisation is that charging of body is always due to  the transfer of electron in integral number. ( means electrons never transfer in fraction or decimal form.) 

Difference between mass and charge 
Charge :
  • Charge is invariant. It is independent of velocity. 
  • Charge causes electromagnetic force. 
  • Charge is quantised. Q = ne; where n is an integer and e is the charge of one electron. 
  • Charge cannot exist without mass. 
  • Charge can either be positive or negative.  
Mass: 
  • Mass is variant, according to Einstein's equation, when a body is travelling with speed comparable to that of light, its mass changes.
  • Mass causes gravitational force.
  • Mass is not quantised. i.e, mass cannot be expressed as integral multiples of a basic unit. 
  • Mass can exist without charge. 
  • Mass is always positive. 

Coulomb's  Law in electrostatic: 
Coulomb's  Law:  Coulomb's law states that the force of attraction or repulsion between two stationary point changes is directly proportional to the product of the magnitudes of the two charges and inversely proportional to the square of the distance between them. 



F∝ `q_{1}``q_{2}`  ---(1)
F∝ `\frac{1}{r^{2}}` -- (2)
F∝  `q_{1}``q_{2}` `\frac{1}{r^{2}}`

F= K  `q_{1}``q_{2}``\frac{1}{r^{2}}`

Where k is the constant of proportionality and is called force constant. K = `\frac{1}{4 πε_{0}}` = 9x10⁹ Nm²C⁻² in SI unit.
F= `\frac{1}{4 πε_{0}}` `\frac{q_{1}q_{2}}{r^{2}}`


`{ε_{0}}` is called absolute permitivity of free space.  
It is equal to 8.854x10⁻¹² farad per meter in free space. 
Unit of permitivity is N⁻¹m⁻²C²
Dimensions of Permittivity: [ M⁻¹ﱣL ⁻³T ⁴A ² ]


Permittivity: 
Permittivity is a measure of how an electric field affects and is affected by a medium.
Limitations of Coulomb's law : It is valid only under the following conditions: - 
1) The electric charges must be at rest. 2) Electric charges must be point charges

Dielectric Constant : The Dielectric constant (K) is defined as  the ratio of the permittivity of the substance to permittivity of the free space (`{ε_{0}}`). i.e. K = ε/`{ε_{0}}` . As Permittivity of medium and permittivity of free space both have same units (F/m i.e. Farad/meter) dielectric constant becomes dimensionless quantity. 

For vacuum or air K = 1 Dielectric constant is also called relative permittivity. Its value is >1 for all media. It is dimensionless quantity. It has no unit.

Coulmb's Law in vector form:

 





As the Colombian forces act along r₁₂ or r₂₁i.e. along the line joining the centers of two charges, so they are central forces.

What is the Principle of Superposition?

The principle of superposition states that every charge in space creates an electric field at point independent of the presence of other charges in that medium. The resultant electric field is a vector sum of the electric field due to individual charges.” 

Continuous Charge Distribution: The continuous distribution of charge may be one dimensional , two dimensional or three dimensional. 
The ways in which charges can be distributed are : 
Linear charge distribution. 
Surface charge distribution. 
Volume charge distribution

Linear charge distribution:  When the charges get distributed uniformly along a length, like around the circumference of a circle or along a straight wire it is called linear charge distribution.



Linear charge density  is defined as charge distributed per unit length, it is  denoted by  λ . 
 λ = q/L 
and it is unit is Coulombs per meter. ( Cm⁻¹)


(b) Surface charge distribution: When the charges get distributed uniformly over the surface , it is called surface  charge distribution.



Surface charge density  is defined as charge distributed per unit area, it is  denoted by  σ . 
σ = q/A  and its unit is Coulombs per meter sqaure. ( Cm⁻²)

Volume charge distribution: When a charge is distributed uniformly over a volume it is said to be volume charge distribution, like distribution of charge inside a sphere, or a cylinder.



  Volume  charge density  is defined as charge distributed per unit volume, it is  denoted by  ρ . 
ρ = q/V  and its unit is Coulombs per meter  cube. ( Cm⁻³). 

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