Electromagnetic Wave Theory

1. Series: EMF Theory
Lecture: #1.10
Dr R S Rao
Professor, ECE
ELECTROSTATICS
Passionate
Teaching
Joyful
Learning
Electric force, Coulomb’s law, point charges, permittivity, Coulomb’s constant,
homogenous medium, isotropic medium.

2. Electrostatics
Coulomb's
Law
2
Coulomb's Law
What is Coulomb's law….
•It describes the force that exists between two stationary
charges of smaller size….
•This force is called electrostatic force or simply electric
force……
•One of the two basic laws of electrostatics ….other one
being Gauss' law…

3. Electrostatics
Coulomb's
Law
3
Coulomb's Law
According to this law, the force on a stationary, point charge due to
another stationary, point charge is:
•directly proportional to the product of the point charges,
•inversely proportional to square of the distance between them,
•along the line joining the point charges.

4. Electrostatics
Coulomb's
Law
4
Coulomb's Law
•repulsion between like charges and attraction in case of unlike
charges,
•inversely proportional to permittivity of the medium, ε
The proportionality constant is 1/4π in MKS system. Most of the
aspects of electric force are known even before Coulomb, his main
contribution is in fixing inverse distance relation for electric force.

5. Coulomb′s law in coordinate-free form.
2
1 ˆ
4
Qq
R


F R
Electrostatics
Coulomb's
Law
5
Coulomb's Law
Mathematically,

6. Electric Force
Electrostatics
Coulomb's
Law
6
Electric force is a force at a distance i.e., the particles do not come into contact
with each other, while exerting or experiencing the force.
• The charge, Q, which is source of the force, is called ′source charge′ and its
location is called ′source point′.
• The charge, q, which is experiencing the force, is called ′test charge′ and its
location is called ′field/observation point′.
• Both the charges must be point charges i.e. their (relative) dimensions must
be negligibly small.
• The test charge q is required to be so small in magnitude, for the validity of
the formula, that the existing field should no way get disturbed by its
presence.

7. Coulomb′s law in terms of position vectors.
Electrostatics
Coulomb's
Law
3
1 ( )
4 | |
Qq




r r'
F
r r'
7
Coulomb's Law

8. Coulomb′s law in Cartesian system.
     
     
3 2
2 2 2
ˆ ˆ ˆ
1
4
Qq x x y y z z
x x y y z z

  
    
 
 

 
  
    
 
x y z
F
Electrostatics
Coulomb's
Law
8
Coulomb's Law

9. 2
1
1 ˆ
4
n
k
k
k k
Q q
R
 
  R
Coulomb′s law for a group of point charges .
1 2
1 2 1 2
2 2 2
1 2
1 ˆ ˆ ˆ
...... .....
4
F = F F F R R R

 
      
 
 
n
n n
n
Q q
Q q Q q
R R R
Electrostatics
Coulomb's
Law
9
Coulomb's Law

10. Electrostatics
Coulomb's
Law
10
Permittivity
The parameter, ε called permittivity represents dielectric nature of medium
in which the charges are located.
• It is a product of two factors, ε=εoεr.
• The first factor is called permittivity of free space and its value is
εo=10–9/ 36π ≈ 8.854×10–12F/m.
• The second factor, a dimensionless quantity, is known as relative
permittivity or dielectric constant of the medium and for free space its
value is one.
• The ratio 1/4π εo is well known as Coulomb′s constant.
• The product 4πεo = 111.11×10–12.

11. Electrostatics
Coulomb's
Law
11
Permittivity
Based on dielectric nature, media can be classified.
• If the permittivity, ε remains same throughout, then the medium
is called homogenous otherwise inhomogeneous.
• The medium is called isotropic, when its ε is a scalar quantity.
For some media, ε is vector and hence, direction dependent: in
such case the media are called anisotropic.
• Media can also be divided into linear and nonlinear based on
permittivity.

12. Point Charges
Electrostatics
Coulomb's
Law
12
• The source charge also experience force due to the test charge and it is,
according to Newton′s third law, equal in magnitude but opposite in direction
to the force due to source charge.
• The point charges need not be in the size of a point, for the validity of
Coulomb′s law. They don′t require to have their absolute dimensions small
or negligible.
• In fact, it requires only that charge sizes be negligible when compared to the
distance between them. It implies that there is no limitation on absolute
dimensions of charges, as long as their relative sizes are negligibly small.

13. Electrostatics
Coulomb's
Law
13
Point Charges
• Coulomb's law describes the force on stationary charge…..another
law is there to describe the electric force on moving charges
….Lorentz force law.
• Coulomb's law….as it is for point charges…but with the help of
superposition principle….it can be extended to other charge
configurations like….line, surface and volume charges.
• A limitation of this law is…..when the distance between the charges is
comparable to size of the charges….it fails completely to predict the
force.

14. ENOUGH
FOR
TODAY
ENOUGH
FOR
TODAY
ENOUGH
FOR
TODAY
ENOUGH
FOR
TODAY
ENOUGH
FOR
TODAY
14