2. Due to the principle of charge conservation, the time
rate of decrease of charge within a given volume must
be equal to the net outward current flow through the
closed surface of the volume.
Thus current Iout coming out of the closed surface is
3. where Qin is the total charge enclosed by the closed
surface. Invoking the divergence theorem
4. Comparing the above equations,
which is called the continuity of current equation.
5. For steady currents,
And hence
showing that the total charge leaving a volume is the
same as the total charge entering it. Kirchhoff's current
law follows from this.
6. To consider the effect of introducing charge at some
interior point of a given material (conductor or
dielectric),
Invoking Ohm’s Law
and Gauss Law,
7. By using the above two laws into Continuity equation,
we get
8. The above equation is a homogeneous linear ordinary
differential equation. By separating variables, we get
And integrating both sides gives,
9. Taking Exponential on both sides
ρv0 is the initial charge density (i.e., ρv at t = 0).
10. The above equation shows that as a result of
introducing charge at some interior point of the
material there is a decay of volume charge density ρv.
The time constant Tr (in seconds) is known as the
Relaxation time or Rearrangement time.
Relaxation time is the time it takes a charge placed in
the interior of a material to drop to e-1=36.8 percent of
its initial value.
11.
12. TEXT BOOKS:
1. William H Hayt and Jr John A Buck, “Engineering
Electromagnetics” , Tata McGraw-Hill Publishing Company
Ltd, New Delhi, 2008
2. Sadiku MH, “Principles of Electromagnetics”, Oxford
University Press Inc, New Delhi, 2009
REFERENCES:
1. David K Cheng, “Field and Wave Electromagnetics”,
Pearson Education Inc, Delhi, 2004
2. John D Kraus and Daniel A Fleisch, “Electromagnetics
with Applications”, McGraw Hill Book Co,
3. Karl E Longman and Sava V Savov, “Fundamentals of
Electromagnetics”, Prentice Hall of India, New Delhi, 2006
4. Ashutosh Pramanic, “Electromagnetism”, Prentice Hall of
India , New Delhi, 2006
