Displacement Current
Maxwell observed that Ampere’s circuital law cannot
be applied between the plates of the capacitor.
When the circuit is closed, conduction current flows
from the plate P of the capacitor to the other plate
through the conducting wires. Maxwell suggested that
due to time varying electric field between the plates,
an electric current, called displacement current (ID),
also flows across the space between the plates of the
capacitor.
Maxwell pointed out that in Ampere’s circuital law, the
current I should be treated as total current i.e., the sum
of the conduction current IC and displacement current
ID and modified the law as 0
.( )
CD
B dl I I
=m+
∫
It is called the Ampere-Maxwell’s circuital law.
The displacement current is defined as
0
E
D
d
I
dt
φ
= ε
( )
0.
DE
EA
I EA
t
ε
= φ=
0
VA V
E
dt d
=ε=
A
V
CC
td
0
ε
= =
Maxwell’s Equations
and Lorentz Force
Gauss’s law of magnetism: It states that the net
magnetic flux crossing any closed surface is always
zero.
Mathematically, .dS 0B=
∫
Maxwell’s Equations
1. 0
/E dA Q= ε
∫
(Gauss’s Law for electricity)
2. 0B dA =
∫
(Gauss’s
Law for magnetism)
3.
–
B
d
Ed dt
Φ
=
∫
(Faraday’s
Law)
4. 0 00
E
c
d
Bd i
dt
Φ
=m +m ε
∫
(Ampere
- Maxwell Law)
Lorentz force: The vector sum of electric force and
magnetic force on any charged particle is called the
Lorentz force.
( )
v
= +×
F qE B
The above five equations give a complete description of
all electromagnetic interactions.
Sources of Electromagnetic
Waves
Neither stationary charges nor charges in uniform motion
(steady currents) can be sources of electromagnetic waves.
The former produces only electrostatic field, while the latter
produces magnetic field that, however, do not vary with time.
It is an important result of Maxwell’s theory that accelerated
charges radiate electromagnetic waves.
The frequency of electromagnetic wave naturally
equals the frequency of oscillation of the charge. The
energy associated with the propagating wave comes at
the expense of the energy of the source-the accelerated
charge.
ELECTROMAGNETIC WAVES
8
Chapter
NCERT CRUX
