chapter 1 class 12 physics Electrostatics

ELECTROSTATICS 

Properties of Charges:

1. There are only two types of charges, i.e, positive and negative.
2. Like charges repel and unlike charges attract each other.
3. Charge is a scalar quantity.
4. Charge is additive in nature. eg. +2 C + 4C =6 C
5. Charge is quantized..
It can be expressed in integral multiples  of fundamental electronic charge
(e = 1.6 x 10-19 C)
q = ± ne where n = 1, 2, 3, …………
6. Charge is conserved.

Coulomb’s Law of electrostatics:

The electrostatic force of interaction (attraction or repulsion) between two point
electric charges is directly proportional to the product of the charges, inversely
proportional to the square of the distance between them and acts along the line
joining the two charges.

F α q1 q2

F α 1 / (r)2
or 
F α  q1 q2/(r)2

F = k q1 q2/(r)2
or
where k is a  constant of proportionality called electrostatic force constant or Coulomb constant.
 
In vacuum, k =1/4πε0
where ε0 is the permittivity of free space




In medium, k =1/4πε
where ε is the absolute electric permittivity of the dielectric medium
The dielectric constant or relative permittivity  is given by

In vacuum,

F =1/4πε0  (q1 q2/(r)2).

In medium,

F =1/4πε0εr(q1 q2/(r)2)


ε0 = 8.8542 x 10-12 C2 N-1 m-2



1/4πε0 = 8.9875 x 109 N m2 C-2

or
 1/4πε0 = 9 x 109 N m2 C-2
  
 dielectric constant,

K = εr =ε/ε0

Units of Charge:

In SI system, the unit of charge is coulomb (C).
One coulomb of charge is that charge which when placed at rest in vacuum at a distance of one metre from an equal and similar stationary charge repels it and is repelled by it with a force of 9 x 109 newton.
In cgs electrostatic system, the unit of charge is ‘statcoulomb’ or ‘esu of charge’.
In cgs electrostatic system, k = 1 / K where K is ‘dielectric constant’.
For vacuum, K = 1.
F =
q1 q2
r2
If q1 = q2 = q (say), r = 1 cm and F = 1 dyne, then q = ± 1 statcoulomb.
In cgs electromagnetic system, the unit of charge is ‘abcoulomb’.

Relative Permittivity or Dielectric Constant :

The dielectric constant or relative permittivity is defined as the ratio of the absolute permittivity of the medium to the permittivity of free space.

Mathematically,k

K = εr =ε/ε0

Continuous Charge Distribution:

A system of closely spaced charges is said to form a continuous charge distribution.they are mainly of three type given below,

(i)                        Linear Charge Density ( λ )

(ii)                   Surface Charge Density ( σ )

(iii)     Volume Charge Density ( ρ )

.

(i) Line or Linear Charge Density ( λ ):

If the charge is distributed over a straight line or over the circumference of a

circle etc, then the distribution is known as‘ linear charge distribution’. It is denoted by λ

( SI unit is C / m)

Mathematically,

Linear charge density is given as,

λ = q/ l

or

λ =dq/dl

Total charge is given by, q = ∫ λ dl.

Surface Charge Density ( σ ):

If the charge is distributed over a surface area, then the distribution is known as

‘Surface charge distribution’.it is denoted by σ .(SI unit is C / m2)

σ =q/S

OR

σ =dq/dS

Surface charge density is the charge per unit area.

Total charge on surface , q = ∫ σ dS

(iii) Volume Charge Density ( ρ ):

If the charge is distributed over a volume, then the distribution is known as

‘Volume charge distribution’.  (SI unit is C / m3)

ρ =q/ז

OR

ρ =dq/d ז

Volume charge density is the charge per unit volume

Total charge on volume, q = ∫ ρ d ז.

Electric Field:

Electric field is a region or space around the charge or a system of charges

within which other charged particles experience electrostatic forces.

.

Electric Field Strength or Electric Field Intensity : Electric field strength at a point in an electric field is defined as the electrostatic force per unit positive charge acting on a  small positive test charge placed at that point.

E=F / q0            (    from coulomb ‘s law  ,   F=1/ 4πε0 (q0 q/ r2 )  r  )

E=1/ 4πε0 (  q/ r2 )  r

 ( r= unit vector of r)

SI unit of electric field is newton / coulomb ( N/C ).

Properties of Electric Lines of Force:

1. The electric lines of force emerge from a positive charge and terminate on    a negative charge

2. The electric lines of force are imaginary lines.

.3. The tangent to an electric field line at any point gives the direction of the electric field  at that point.

4. Two electric lines of force can never cross each other. If they do so, then at the point of

intersection, there will be two tangents. It means there are two direction of the electric field at that point, which is  impossible

5. Electric lines of force are closer where the electric field is stronger and the lines spread

out where the electric field is weak.

Electric Dipole:

Electric dipole is a pair of equal and opposite charges separated by a very

small distance.

Electric dipole moment is denoted by p,

p = (q x 2l)

The magnitude of electric dipole moment is the product of magnitude of  either charge and the distance between the two charges.

 SI unit of p is coulomb metre (C m). and it is a vector quantity.

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GUASS THEOREM  FOR CLASS 12