engineering physics

1. Name : Shubhajit Chatterjee.
Student Code : BWU/BEC/19/028.
Course Name :Electromagnetism and Field Theory.
Course code :BSC(ECE)301.
Program : Bachelor of Technology in Electronics & Communication Engineering.
Semester : 3rd Semester.
Topic: Maxwell’s Four Equations In EM Theory

2. MAXWELL’S EQUATIONS
In 1865, James Clerk Maxwell (1831-1879) published A
Dynamical Theory of the Electrodynamic Field, which
featured the original set of what is now referred to as
Maxwell's equations.
Through these equations, Maxwell described
scientifically the propagation of light and
electromagnetic waves travelling through space at the
speed of light.
These equations are:
1) Gauss’s law in electrostatics.
2) Gauss’s law in magnetostatics .
3) Faraday’s law of electromagnetic induction
4) Ampere’s law with Maxwell’s correction.
1

3. Maxwell’s Equation In Differential Form
 Maxwell’s 1st Equation:
  Maxwell’s 2nd Equation:
𝛻 ⋅ 𝐵 = 0
   Maxwell’s 3rd Equation:
    Maxwell’s 4th Equation:
𝛻 × 𝐸 = −
𝜕𝐵
𝜕𝑡
𝛻 × 𝐵 = 𝜇0 J +
𝜕𝐷
𝜕𝑡
= 𝜇0 J + 𝜀0
𝜕𝐸
𝜕𝑡
𝛻 ⋅ 𝐸 =
𝜌
𝜀0
2
The 1st equation represents Gauss’ law
in electrostatics.
The 2nd equation is represents Gauss’ law
in magnetostatics .
The 3rd equation is represents Faraday’s
law of electromagnetic induction .
The 4th equation is represents modified
ampere’s(Ampere’s law with Maxwell’s
correction) .

4. Maxwell’s Equation In Integral Form
3

5. Physical Significance of Maxwell’s equations
 Maxwell’s 1st Equation:
 Maxwell’s 2nd Equation:
4
a) Steady state equation.
b) Total electric flux through any close surface is
1
𝜀0
time the
total charge include with in the surface.
c) Electric field lines start from positive charges and end at
negative charge.

6.  Maxwell’s 3rd Equation:
 Maxwell’s 4th Equation:
5

7. 𝜌 = 0, 𝐽 = 𝜎𝐸 = 0, 𝐵 = 𝜇0 𝐻
𝛻 ⋅ 𝐸 = 0
𝛻 ⋅ 𝐵 = 0
𝛻 × 𝐸 = −
𝜕𝐵
𝜕𝑡
= − 𝜇0
𝜕𝐻
𝜕𝑡
𝛻 × 𝐵 = 𝜇0
𝜕𝐷
𝜕𝑡
In free space ,the following physical conditions are satisfied
Under these condition, Maxwell’s equations take the following
form:
6
(2)
(1)
(3)
(4)

8. 7
𝜕𝐵
𝜕𝑡
= 0,
𝜕𝐷
𝜕𝑡
= 0
𝛻 ⋅ 𝐸 =
𝜌
𝜀0
𝛻 ⋅ 𝐵 = 0
𝛻 × 𝐸 = 0
𝛻 × 𝐵 = 𝜇0 𝐽
 For static field conditions are
 Under these condition, Maxwell’s equations take the
following form:
(1)
(4)
(3)
(2)

9. 8