PPT - Poynting Theorem Electrical Engineering (EE) Notes | EduRev

 Page 1


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