EMS
Summary
Lecture
is
Îiz
1 9192
The force depends on distance : ( Coulomb's Law :) Ez =
4e Eo TE Êz
field > ☐
☐ %
dont
streng of
Eo the electric others
permitivity certain Materials permit as as
•
is ,
an .
Zo Ê
Î the vector from tot Â
is
painting charge
•
, 2 2 .
÷
in =
tril % ° '
t 92
Electric of position of qi : E- riz Îiz
Feld
charge 92 in 4 # Eo
Force by electric Field of charge 92 F- =
91E
acting on
q , :
/motion
The fixed Coulomb '
s Law ,
which takes into account the tinne; The
Feynman's equation :
'
9 er> r d er ' 1 dz
( )
-
E- =
4# Eo [r > 2
+ cdt r
"
+ czdtz er >
7-
Flux : ∅ =
# (r ) .
da = ver > 11daL cos ( Q)
,
with D-
being the
angle between the Field vector and the Surface
normal vector So the flux wilt with COSLQ)
.
charge .
G- ans 's law which equates the flux to the volume
Integral of the
divergente of the fieldi
dvx dus dvz
I. ✓ ( r ) Jz
2x +
J +
=
Lecture 2
I. È = % ,
the È Field has non -
zero
divergence . . .
where there is non -
Zero
charge density .
# E. VI. Èdv
Qenc
Gauss's law : da = = Êodv = Eo
(url & Stokes 's Theorem :
• )/ ✗ f. da
• § f. dr
•
G- radient : ITVCR)
42 Ver)
Diuergence
•
_
:
•
Curt : IX Tkr)
ij
, Lecture 3
1 QQ 920
Superpositie : ËË Ê + . . .
=
4 # Eo ( ri Î + ri rit . . .
)
F- =
QË
N qi
Ê
1
=
4 # Eo riz Ê
Line dq
'
1dL ' [ Clm ] (
charge per unit length )
charge element :
•
-
=
KÈ )
✓
'
Ë4
'
# {☐ rz Edl '
•
Surface -
charge element : dq
' =
ods
'
[ C / ni ] ( chare
per unit area )
Joeri
1 )
Ë4 # {• rz Fda
'
9
Volume charge volume )
'
=p de [ Clm' ] (
'
•
-
element : dq charge per unit
PCRÌ
E- 4*1<0 / rz ÎDT
'
Q -1L ,
Q -
_
al ,
② =p L
Coulomb's Law in relation with Gauss's law : Flux of electric field through a Snrface :
Ole =/ È -
dà
S
Flux closed Surface : the Total nettamount
charge
Integral over a Measure of of
Insider the enclosed volume .
dat = ( rsinodokrd G) Î
§ Ëdâ %
ZIT JT
IÉEOÎ '
rzsinododocr F) . = =
# Ëda
Qenc
Gauss's Law :
Integral to differential : = È Ëdv . = Êodv =
Eo
Gauss's Law in differential form : Ë Ê - = ÉOP
With Gauss's Law the Field the distribution
we can Calculator From
charge in
very Special situation .
Gauss's Law →
spherical Symmetry : #Ë '
dà = E- 4#
'
r = È Êdv .
Uniform
ly
>
P
% DV
P -4
>
1 R
Charged
•
Outside : E. Uar '
= =
TE 3 # R E- =
Eo 3 rz Sphere
P
% dv Ê
1
Insider:
>
E.
'
•
Uar = =
r =>
E- Eo 3 r
Curt of electroStatic Field (Stokes '
Tneorem) : ÊXÊ ) dà -
=
# È dl -
'
•
È ✗ Ë -0 (only for staties)
b
Ë = -
4- ¢
{Ëdl =
(rct ,) ) -
¢ Crctz))
Summary
Lecture
is
Îiz
1 9192
The force depends on distance : ( Coulomb's Law :) Ez =
4e Eo TE Êz
field > ☐
☐ %
dont
streng of
Eo the electric others
permitivity certain Materials permit as as
•
is ,
an .
Zo Ê
Î the vector from tot Â
is
painting charge
•
, 2 2 .
÷
in =
tril % ° '
t 92
Electric of position of qi : E- riz Îiz
Feld
charge 92 in 4 # Eo
Force by electric Field of charge 92 F- =
91E
acting on
q , :
/motion
The fixed Coulomb '
s Law ,
which takes into account the tinne; The
Feynman's equation :
'
9 er> r d er ' 1 dz
( )
-
E- =
4# Eo [r > 2
+ cdt r
"
+ czdtz er >
7-
Flux : ∅ =
# (r ) .
da = ver > 11daL cos ( Q)
,
with D-
being the
angle between the Field vector and the Surface
normal vector So the flux wilt with COSLQ)
.
charge .
G- ans 's law which equates the flux to the volume
Integral of the
divergente of the fieldi
dvx dus dvz
I. ✓ ( r ) Jz
2x +
J +
=
Lecture 2
I. È = % ,
the È Field has non -
zero
divergence . . .
where there is non -
Zero
charge density .
# E. VI. Èdv
Qenc
Gauss's law : da = = Êodv = Eo
(url & Stokes 's Theorem :
• )/ ✗ f. da
• § f. dr
•
G- radient : ITVCR)
42 Ver)
Diuergence
•
_
:
•
Curt : IX Tkr)
ij
, Lecture 3
1 QQ 920
Superpositie : ËË Ê + . . .
=
4 # Eo ( ri Î + ri rit . . .
)
F- =
QË
N qi
Ê
1
=
4 # Eo riz Ê
Line dq
'
1dL ' [ Clm ] (
charge per unit length )
charge element :
•
-
=
KÈ )
✓
'
Ë4
'
# {☐ rz Edl '
•
Surface -
charge element : dq
' =
ods
'
[ C / ni ] ( chare
per unit area )
Joeri
1 )
Ë4 # {• rz Fda
'
9
Volume charge volume )
'
=p de [ Clm' ] (
'
•
-
element : dq charge per unit
PCRÌ
E- 4*1<0 / rz ÎDT
'
Q -1L ,
Q -
_
al ,
② =p L
Coulomb's Law in relation with Gauss's law : Flux of electric field through a Snrface :
Ole =/ È -
dà
S
Flux closed Surface : the Total nettamount
charge
Integral over a Measure of of
Insider the enclosed volume .
dat = ( rsinodokrd G) Î
§ Ëdâ %
ZIT JT
IÉEOÎ '
rzsinododocr F) . = =
# Ëda
Qenc
Gauss's Law :
Integral to differential : = È Ëdv . = Êodv =
Eo
Gauss's Law in differential form : Ë Ê - = ÉOP
With Gauss's Law the Field the distribution
we can Calculator From
charge in
very Special situation .
Gauss's Law →
spherical Symmetry : #Ë '
dà = E- 4#
'
r = È Êdv .
Uniform
ly
>
P
% DV
P -4
>
1 R
Charged
•
Outside : E. Uar '
= =
TE 3 # R E- =
Eo 3 rz Sphere
P
% dv Ê
1
Insider:
>
E.
'
•
Uar = =
r =>
E- Eo 3 r
Curt of electroStatic Field (Stokes '
Tneorem) : ÊXÊ ) dà -
=
# È dl -
'
•
È ✗ Ë -0 (only for staties)
b
Ë = -
4- ¢
{Ëdl =
(rct ,) ) -
¢ Crctz))
