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Displacement Current updated Copy.ppt
1.
2. Books
Text Book:
1. PRINCIPLES OF ELECTROMAGNETICS
By - MATTHEW N.O. SADIKU, 4th 2009 OXFORD UNIVERSITY
PRESS, INDIA
Reference Book:
1. ELECTROMAGNETIC WAVES AND RADIATING SYSTEMS
By - EDWARD C. JORDAN 5th PRENTICE HALL
3. Displacement Current
In the previous section, we have essentially reconsidered
Maxwell's curl equation for electrostatic fields and modified it
for time-varying situations to satisfy Faraday's law. We shall now
reconsider Maxwell's curl equation for magnetic fields (Ampere's
circuit law) for time-varying conditions.
For static EM fields, we recall that
But the divergence of the curl of any vector field is identically
zero,Hence:
The continuity of current in eq. , however, requires that
4. Thus both the eqs are obviously incompatible for time-varying
conditions.
We must modify the Ampere Circuit law
To do this, we add a term in the eq. of Amp Circuit law so that it
becomes
Where is to be determined and defined. Again, the
divergence of the curl of any vector is zero. Hence:
5. Substituting in equation
This is Maxwell's equation (based on Ampere's circuit law) for a
time-varying field. The term Jd = dD/dt is known as
displacement current density and J is the conduction
currentdensity ( ).
6. Based on the displacement current density, we define
the displacement current as
where I is the current through the conductor and S1 is
the flat surface bounded by L.
If we use the balloon-shaped surface S2 that passes
between the capacitor plates, as in Figure
7.
8. because no conduction current (J = 0) flows through S2
This is contradictory in view of the fact that the same closed path
L is used. To resolve the conflict, we need to include the
displacement current in Ampere's circuit law. The total current
density is
Now the equations remains valid.
So we obtain the same current for either surface though it is
conduction current in S1 and displacement current in S2.
