Transcript Unit-III electromagnetics-1x

ELECTROMAGNETICS
Poynting Theorem, Poynting vector
and its’ Physical significance.
By
Dr Ajay Kumar Sharma
Hindustan Institute of Technology & Mgmt., Agra
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INTRODUCTION
Electromagnetic Energy: Poynting Theorem
• Elect. P.E=
• Magnet. P.E=
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U e   E.Ddv
2v
1
U m   H .Bdv
2v
B
 E  
t
D
 H  J 
t
Poynting
H .  E   H .
B
t
D 

E.  H  E. J 

t 

.E  H   H .  E  E.  H
B
D
.E  H    H .
 E.
 E. J
t
t
2
H .  E  E.  H
B
D
 H .
 E.
 E. J
t
t
D
 E   E 2
E.
 E.

t
t
2 t
B
 H   H 2
H.
 H.

t
t
2 t
.E  H   H .  E  E.  H
B
D
. E  H    H .
 E.
 E. J
t
t
D
 E   E 2
E.
 E.

t
t
2 t
B
 H   H 2
H.
 H.

t
t
2 t
 1



E
.
D

H
.
B
 E. J


t  2

 1






.
E

H
dv


E
.
D

H
.
B
v
v t  2
dv   E.Jdv
v
 1





E

H
.
ds


E
.
D

H
.
B
dv   E.Jdv




t v  2

v
.E  H   
Rate of energy trasf.into
the EM field through the
motion of free charge
in vol v
Rate of change of EM energy stored in vol.v
EM energy crossing the closed surface per second
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Applications of Poynting Theorem
• The Poynting vector in a coaxial cable
For example, the Poynting vector within the dielectric insulator of a coaxial cable is
nearly parallel to the wire axis (assuming no fields outside the cable) - so electric
energy is flowing through the dielectric between the conductors. If the core conductor
was replaced by a wire having significant resistance, then the Poynting vector would
become tilted toward that wire, indicating that energy flows from the
electromagnetic field into the wire, producing resistive Joule heating in the wire.
• The Poynting vector in plane waves
In a propagating sinusoidal electromagnetic plane wave of a fixed frequency, the
Poynting vector oscillates, always pointing in the direction of propagation.
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• DC Power flow in a concentric cable
Application of Poynting's Theorem to a concentric cable carrying DC current leads to the
correct power transfer equation P = VI, where V is the potential difference
between the cable and ground, I is the current carried by the cable.
This power flows through the surrounding dielectric, and not through the cable
itself. However, it is also known that power cannot be radiated without accelerated
charges, i.e. time varying currents. Since we are considering DC (time invariant) currents
here, radiation is not possible. This has led to speculation that Poynting Vector may not
represent the power flow in certain systems.
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References
Introduction to Electrodynamics by
David. J. Griffith : Pearson Education Publication
Engineering Physics-II by
Satya Prakash :Pragati Prakashan
Enginnering Physics-II
by S.K.Gupta :
websites: www.nptel.in ,
www.wikipedia free encyclopedia.
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