PPT: Poynting Theorem | Electromagnetic Fields Theory (EMFT) - Electrical Engineering (EE) PDF Download

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Poynting’s Theorem Poynting’s Theorem
… energy conservation … energy conservation
John Henry Poynting (1852-1914)
Page 2


Poynting’s Theorem Poynting’s Theorem
… energy conservation … energy conservation
John Henry Poynting (1852-1914)
To recap… To recap…
nn The energy stored in an electric field E is The energy stored in an electric field E is
expressed as the work needed to “assemble” a expressed as the work needed to “assemble” a
group of point charges group of point charges
2
1
2
2
1
2
Eo
Eo
uE
W E dV
e
e
=
=
ò
Page 3


Poynting’s Theorem Poynting’s Theorem
… energy conservation … energy conservation
John Henry Poynting (1852-1914)
To recap… To recap…
nn The energy stored in an electric field E is The energy stored in an electric field E is
expressed as the work needed to “assemble” a expressed as the work needed to “assemble” a
group of point charges group of point charges
2
1
2
2
1
2
Eo
Eo
uE
W E dV
e
e
=
=
ò
nn Magnetic fields also store energy Magnetic fields also store energy
nn Total energy stored by electromagnetic fields per unit Total energy stored by electromagnetic fields per unit
volume is… volume is…
2
1
2
2
1
2
o
o
B
B
uB
W B dV
m
m
=
=
ò
22
11
()
2
o
o
u EB e
m
=+
Page 4


Poynting’s Theorem Poynting’s Theorem
… energy conservation … energy conservation
John Henry Poynting (1852-1914)
To recap… To recap…
nn The energy stored in an electric field E is The energy stored in an electric field E is
expressed as the work needed to “assemble” a expressed as the work needed to “assemble” a
group of point charges group of point charges
2
1
2
2
1
2
Eo
Eo
uE
W E dV
e
e
=
=
ò
nn Magnetic fields also store energy Magnetic fields also store energy
nn Total energy stored by electromagnetic fields per unit Total energy stored by electromagnetic fields per unit
volume is… volume is…
2
1
2
2
1
2
o
o
B
B
uB
W B dV
m
m
=
=
ò
22
11
()
2
o
o
u EB e
m
=+
Work done moving a charge… Work done moving a charge…
nn Use the Lorentz formula: Use the Lorentz formula:
nn The work in time The work in time- -interval dt is then: interval dt is then:
() F qE vB = +´
() dW F dl q E v B dl qE vdt = ×= + ´ ×= ×
(remember: Magnetic fields do no work!)
Page 5


Poynting’s Theorem Poynting’s Theorem
… energy conservation … energy conservation
John Henry Poynting (1852-1914)
To recap… To recap…
nn The energy stored in an electric field E is The energy stored in an electric field E is
expressed as the work needed to “assemble” a expressed as the work needed to “assemble” a
group of point charges group of point charges
2
1
2
2
1
2
Eo
Eo
uE
W E dV
e
e
=
=
ò
nn Magnetic fields also store energy Magnetic fields also store energy
nn Total energy stored by electromagnetic fields per unit Total energy stored by electromagnetic fields per unit
volume is… volume is…
2
1
2
2
1
2
o
o
B
B
uB
W B dV
m
m
=
=
ò
22
11
()
2
o
o
u EB e
m
=+
Work done moving a charge… Work done moving a charge…
nn Use the Lorentz formula: Use the Lorentz formula:
nn The work in time The work in time- -interval dt is then: interval dt is then:
() F qE vB = +´
() dW F dl q E v B dl qE vdt = ×= + ´ ×= ×
(remember: Magnetic fields do no work!)
nn Remember current density J!  The moving Remember current density J!  The moving
charge or charges constitute a current charge or charges constitute a current
density, so we can write density, so we can write
which means the work can now be which means the work can now be
expressed as expressed as
qE vdt E J × =×
()
dW
E J dV
dt
=×
ò
Remember that this is a rate of change of the energy (work) and so
represents power  delivered per unit volume
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FAQs on PPT: Poynting Theorem - Electromagnetic Fields Theory (EMFT) - Electrical Engineering (EE)

1. What is the Poynting Theorem?
Ans. The Poynting Theorem is a fundamental concept in electromagnetics that relates the flow of electromagnetic energy in a given region to the electric and magnetic fields present in that region.
2. How is the Poynting Theorem derived?
Ans. The Poynting Theorem is derived from Maxwell's equations, specifically from the time-averaged form of the equations. It involves taking the dot product of the electric field vector and the magnetic field vector, integrating over a closed surface, and applying the divergence theorem.
3. What does the Poynting Theorem state about energy flow?
Ans. The Poynting Theorem states that the rate of energy flow through a given surface is proportional to the vector product of the electric and magnetic fields at any point on that surface. It also indicates the direction of energy flow, which is perpendicular to both the electric and magnetic fields.
4. How is the Poynting Theorem applied in practical scenarios?
Ans. The Poynting Theorem is widely used in various areas of electromagnetics, such as antenna theory, microwave engineering, and electromagnetic compatibility analysis. It helps in understanding the power distribution, radiation patterns, and energy transfer in these systems.
5. Can the Poynting Theorem be extended to other forms of energy?
Ans. Yes, the Poynting Theorem can be extended to other forms of energy, not just electromagnetic energy. By considering the appropriate fields and their interactions, the theorem can be applied to other types of energy flow, such as acoustic energy or fluid flow in certain cases.
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