-19
e = 1.602 × 10 ( C )
; 
= 
· dr ;;
F· dr == F · (dr/dt) dt
û[] + dz û[z]dz û[r] + dr dz û[] + r dr d û[z] dz ) d û[] + r d
û[]) dd û[r] + r dr d û[] + r sin() dr d û[] ) dr dd· E 
= E · dA == E · n dS
== ¹ + ² + ... = 
E· dA dum campo E através da superfície S de um volume elementar V == 
(· E ) dV E· dA = Q/
=(1/r² ) r · dA = (1/r) · n dS
q 1
E == ------[-] == - ==> E· dr == -
4
r
= Trabalho / Carga = 2 
log(r) = 2
[(y²+a²)^½ y]
1 q¹q²
W == ------- ---------
12 4 |r¹ - r²|
q q
1 1 i j
W == - 
------- ---------
2 4 |r - r |
i j
1 
[r] [r'] 1
W == - ( ------------ dV)dV' == - [r] [r] dV
2 |r - r'| 2
(· E) dV == ½E · dV == ½|E|² dV 
dV
onde a densidade de energia é == ½|E|² E· dS == · E dV == Q[int]/
Q[int]/== [r]/dV ==> · E == /
==> · E == ² == / E· dr == × E· dS == ( 1/ 4) Q/R ==> C == 4 R/ ==> == (/) d ; Q == A ==> C == A/d
c
k T i
== --- Log[--]
N q c
e o
-23 J -19
k == 1.38 × 10 ( - ); q == 1.6 × 10 ( C )
K e
S E == ½ E² S ==> ½ (/d)² S == m g
2
1 1 Q 1 2
dW == (q) dq == - q dq ==> W == dW == - -- == - C
C 2 C 2
¹ == ² == ... == ¹ + ² + ... == 
== E · dr [pol] == P· n[pol] == · P E + P ==> · D == [livre]
E tem-se (1+) E == 
E == E == 1 + == == ½ E· D dVW/t == · J + s Densidade volumica da grandeza Z
T - T
1 2
G == 2 K L -------
b
ln[-]
a
G G
T[r] == --------- + --------- com r == r - r e r == r + r
4 K r 4 K r 1 G 2 G
1 2
Q == It J· dS
Massa Molecular Densidade Volume Molar
g g M cm³
M == 63.5 --- == 8.95 --- V == -- == 7.09 ---
mol cm³ mol
Q == I t == n e v· S t ==> v· n == 0.246 mm / s == R I
) Ohm == Volt / Ampére (m) = Resistência de um cubo de lado unitário (mhO/m) = 1 / == (1 / R) · dr == (1 / R) E· dr ) E == E == E· dr == == [+] [-]¹== q / C² == R dq/dt == ¹ ²
1 dq
== - q + R --
C dt
t
- --
CR
q[t] == C( 1 - e )
I[n] ==0 [n] == 0 == R I²· B == 0
o/(4) I (dl × r) / r ³o/(2) I/ R
] é a distância do ponto ao condutoro/(2) I I'/ d
o I R²
B == -------------- e
3/2 z
2 (R² + z²)
B· dr == o (I¹+I²+I³+ ...) (× B)· dS == B· dr == o (I¹+I²+I³+ ...) == o J· dS × B == o J B· dr == B L == o (n L) I ==> B == o n I
b - lados da espira (centrada na origem)
[a] == a × (2I b × B) == 2I ( (a· B) b (a· b) B)[b] == b × (( 2I a) × B) == 2I ( (b· B) a + (a· b) B)[a] == ( a) × (( 2I b) × B) == 2I ( (a· B) b (a· b) B)[b] == ( b) × ( 2I a × B) == 2I ( (b· B) a + (a· b) B) == 4 I ( (a· B)b (b· B)a ) == 4 I (a × b) × B == m × B == m × B dr × B == I (B· n) dS == df (B· n) dS == r × ( I dr × B) == (dm × B) + (r × df )(B· n) ==0 tem-se == (dm × B) == m × B dm == IdS == IS n == J B d /(n q) v
== qB/(2m)× A garante que · B == · (× A) 
0× (× A) ==(· A) - ² A× A == × (A + 
) para qualquer , porque × () 0· A == 0. solução de ² == -· A', e usa-se A == A' + )· A == 0)× B ==(· A ) - ² A == - ² A ==o J
o J[r']
A[r] == ---- ------ dV'
4 |r-r'|
1
B == B û ==> A[r] == - B × r
o z 2
a² :
I o
J == ---- û ==> A[r] == ---- I Log[r] û
a² z 2 z
2
o n I a
J == J û ==> A[r] == --- ------ û
o 2 r
a² I n)
o dr' o 1
A[r] == --- I -------- ==> A[r] == --- ------ m × û
4 |r - r'| 4 2 r
r
o M[m] H (válido para materiais não-ferromagnéticos): == o(1+[m]) tem-se B == H[m] ~ 10^-6 < 0 == o(1+[m]) ~ o[m] ~ 10^-6 >0 == o(1+[m]) ~ o ~ 10^9 × o J· A dV == ½ B· H dV
o dm × r o M × r
dA == --- ------ == --- ----- dV
4 r³ 4 r³
o M[r']×(r-r')
A == dA == --- ------------ dV'
V' 4 V' |r-r'|³
1 1 r - r'
× ------ == -('× ------) == -------
|r-r'| |r-r'| |r-r'|³
V' designa a superfície fronteira de V')
o M[r']× dS' o '× M[r']
A == --- ---------- + --- ---------- dV'
4 V' |r-r'| 4 V' |r-r'|
o J[r']
A == --- ------ dV'
4 V' |r-r'|
× M : Densidade de Corrente (em volume)V'×B == o J[cond] + o J[mag] == o (J[cond] + ×M) ×(B/o M) == × H == J[cond]·D == [livre] onde D == E + P. H·drx espessura da fendar == /o permabilidade magnética relativa do entre-ferro
N r
B = o - I -----------
ext L x
1 + r ---
L
== E¹· dr == B·dS
d
== ---
dt
d
== E¹· dr == × E¹ ·dS == (B/t )·dS
d B
== --- == (v[r]×B[r]).dr ---·dS
dt t
× E¹ == B/t¹ ==² == : fluxo numa espira qualquer == ¹ : fluxo no primário == ² : fluxo no secundário
N
d d ¹
== N --- ; == N --- ==> == --
¹ ¹ dt ² ² dt ¹ N ²
²
× A × E + B / t == 0 == × (E + A / t ) A / t == A / t == B· dS == A· dro/(4) J[ r'] × ( r r') / | r r'| ³ dV' == o/(4) I' dr' × ( r r') / | r r'| ³ o/(4) J[ r'] / | r r'| dV' == o/(4) I' dr'/ | r r'|
o 1
== L I + A [r ]·dr == L I + (--- I --------- dr )·dr
i i i i k
i k i i i i i ki 4 k k |r - r | k i
i k
o 1
L == --- ( --------- dS × (r - r ))·dr
i 4 i |r - r |³ i i
i
o 1
M == --- --------- dr ·dr
ik 4 i k |r - r | k i
i k
d d
== L --I - M --I
i i dt i ki ik dt k
,A] (Lei de Ohm),A] == A / t = E[f.e.m.]·dr == (E[TOTAL] E[,A])·dr == (J / ) ·dr + ( ) ·dr + (A / t )·dr == Jl / + + d / dt == R I + (1/C) I dt + L dI / dt == E d == D d / == D A / C == Q/ C A / d I dt == A·dr == LI)
it
I[t] == I e
o
i
[t] == R I[t] - --- I[t] + iL I[t] == Z I[t]
C
1
Z == R + i (L - ---)
C
× H == J implicaria ·J == · (× H ) 0 (?)·J == /t == · (D /t ) nem sempre 0 mas·( J + D /t ) 0D /t à lei de Ampére× H == J + D /t × E == B / t× H == J + D / t· D== [cond]· B == 0, A A / t× A E E H E + P ~= E o M ~= B/ [pol] == · P [pol] == P· n × M (A / m²) E; J = E) onde = 1/c²× (× E) == (· E) ² E == (× B) / t == J / t ² E / t ²² E == (/) + E / t + (1/c²) ² E / t ²× (× B) == (· B) ² B == ( × J + (× D) / t ) == × E + (× E) / t ² B == B / t + (1/c²) ² B / t ²