-
Cylindrical
.
(1
,
0
--
7)
,
p
=
P
X
dSq
dsz
1dadz
=
drdz
=
=
rdrdq
dr
=
2
y
#
when
(v
,
O
b)
,
X
Z
-
=
y
=
z
=
r
=
=
.
identify
. write
2
formula
general rector
I
(Axcosa + AysinG)ap
* (r 0
=
,
cost y
A
uk is
calculating
4)
-
z
3. find
+
( AxsinG
-
(AxsinEcos + AysinsinPar
=
-
=
do
source
dSr
Rsindodd
=
dSo
=
E =
.
(d orf(d
x))ax
(y
+
line
TER3
da
dsa
=
law
at
prime
-
y)ay
+
(z
$
D
.
(x , y't') coordinates
(source)
based
-
z)e
=
Surface :
lede
da
=
volume :
dazerdu
esds
=
+
+
/AXcoscos +
AycosOsind-AtsinGa
Exo-line charge
-charge
:
o
:
=
leaza
+
physical
on
ds =
Gene
=
(f) ev
-
spherical symmetry :
cylindrical symmetry
du
9) . /Dds
s =
=
Dpds
=
Gene-radius based
on
er
actual
Surface
Dry d
radius of
=
D(4
I
e
gaussian
:
of
ganss surface
surface
tips :
gaussian
cort
-
as
r
more
surface
or
regions
den .
2
E(at z27312
surface
.
Aycos()aq (Az)z
Eoline
based on gaussian
8 5
+
surface
--
②
A -4z
(xax yay)
charge :
-
①
Azaz
↑
varde
or())d)
Suss
A ad
+
+
dQπ
-
X-al
Eplane along x-y
rsinGdrdd
i
4
4
Aq
↑
1-AxsinP + Axcos0) ad
field de
infinitesimal
d
(x
+
↑
surpace
-
.
i and
=
Apay
=
Ayay + At Az
tan"
gauss except
E
:
Axax +
=
I
+
+
+
for
tan" (3)
de
x
y z2
infinitesimal
the
*
=
,
.
>
-
distribution
1
D
>
-
O
,
~Cos E
spherical symm
#used for
(X y z)
identified
at
using sind
resinodadr
kin for
point
2
G
,
* used when
cos Q
8
I
cost
using
=
P
O
-
I find
calculating
Gin for cyl symmetry
#used in gauss except
dV
=
z =Z
② spherical
sinQ
1
.
3
psing
pdedodzused
=
az
2ay
+
PCOS@
=
az
sing
ay
jax
1
aq
Cost
1
Z
=
1
ap
1
ax
tan
=
i
X
&Sp
My 2
2 =
·
Cookbook :
,
stays same no
of
gaussian
recalculate
sur .
Gene
need
to
recalculate
as
more
across
diff regions
since
defined
Penta
ray
·
=
e
&
v(x , y , z)
an
infinitesimal
and
its
location
single point
2.
write
3
Find
.
R
du
z
-
=
2
+
G
=
YoR
. Integrate
4
(y yz)2
=
charge da (gudv , esds , ledel
xxi
=N
(y-jTz-z')2
R
+
charge distribution
arbitrary
an
1. find
G
=
to
cookbook :
I
-d
potential
due
potential
·
do
f d
=
-
i
Ec
the
over
charge distribution
-
E
Suc
=
Tv
-
v
=
)dr fe
=
capacitance
per unit
A cable
< plate =
C parallel =
C + (2 +...
I
=+
(series
b
a
Ez
4
length :
a
+
...
Cepnere
2π6
=
Iibla)
=
b= 0
Minab
=
)
Ea
El
El
conditions
any
·
DneWS-Dn , S
eg : normal :
tangential
-it
-
En
Estance
Eatanol
=
=
E an
Etani
E . -Eni an
=
eg
=
Dri
:
.
identify
the
infinitesimal
2 write formula
.
general rector
3. find
:
E
=
(x
-
x))ax
=
.
E =
prime
+
(y
line
TER3
da
E
-
y)ay
+
(z
-
=
charge :
surface :
lede
da
=
volume :
2
dazerdu
esds
=
=
>
-
i
·
:
(5 ds (r ) (d
.
=
94-me
Oke
z)e
(d orf(d- or())d)
integrals
animal
(x , y',z) coordinates
(source
i
dQπ
4
4
at
Enta
field de
infinitesimal
d
i and
for
source
EiEi
or
=
E
field
-electric
1
no
es
- 15 = 0 :
EiE2
Dnz
Enz
=
+
-
+
energy
we
=
z)vdv
Potential
=
Com