Static magnetic fields

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Maxwell's equations Poynting's theorem boundary
conditions
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constitutive relations

• D ??E?
• B ??H
• j ??E

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Poyntings theorem
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Poyntings theorem

• em power that leaves
• - ?(stored em energy) / ?t
• - lost em power

E x H
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Spherical radiation

• E x H ds EH 4??2
• ? E2 4??2
• ? constant
• E ? 1/?

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Cylindrical radiation

• E x H ds EH 2?r L
• ? E2 2?r L
• ? constant
• E ? 1/(r)1/2

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2?rH?
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Boundary conditions
components
Pillbox ?S
Loop ?L
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Integral form of Maxwells equations
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Normal component of B
Bn1?s Bn2 ?s 0
Normal components of B are continuous
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Normal component of D
Dn1?s Dn2 ?s ?s ?s
Normal components of D differ by surface charge
density
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Tangential component of H
Ht1?L Ht2 ?L js ?L
Tangential components of H differ by surface
current density
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Tangential component of E
Et1?L Et2 ?L 0
Tangential components of E are continuous
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example
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example
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example
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boundary conditions for time varying fields
Tangential components of the electric field
intensity are continuous
Normal components of the displacement flux
density differ by a surface charge density
Tangential components of the magnetic field
intensity differ by a surface current density
Normal components of the magnetic flux density
are continuous
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Tangential component of Emetal ? ? ?
Et1?L Et2 ?L 0
but Et2 0
Tangential component of E is zero.
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images

• Charge Q
• Equipotential contours
• Electric field E

• Image charge -Q
• Equipotential contours
• Electric field E

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images
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• Image charge Q

• Image charge Q

• Charge Q

2d

• Image charge -Q

• Image charge Q

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Antenna on top of the ground

• Underneath an antenna is an array of conductors
• This creates a ground plane
• This effectively makes the antenna twice as tall

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microwave oven
magnetron
roast
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microwave oven
local hot spot
magnetron
roast
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microwave oven
whirly blade
components

magnetron
roast
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microwave oven
whirly blade
magnetron
roast
metal
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CD
an egg before
microwave oven experiments -- dangerous
an egg after
tooth pick
aluminum foil
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