Electricidad

Campo Eléctrico
r
qq
1 q1 q 2
1
Nm 2
ˆ
ˆ
F = k 1 2 2 ur =
u r donde k =
= 9.0 × 10 9
4πε o r 2
4πε o
r
C2

rr
Φ E = ∫ E ⋅ dA



qˆ
 k 2 ur 
r
 λ dl linear charge 

r
qi




ˆ
E = k ∑ 2 u ri  donde dq =  σ dA surface charge 
ri


 ρ dV volume charge

dq


ˆ
k ∫ 2 ur 

r


r q enc
r
∆U = −Wsist
∫ E ⋅ dA =

rr
Wsist = q ∫ E ⋅ ds

∆V =

r
r
F
E = lim
q →0 q

εo

brr
∆V = V (b) − V (a ) = − ∫ E ⋅ ds

∆U
q

a

r r

− ∫ E ⋅ ds 


∞
q

 λdl 


 kr 
V =
 donde dq =  σdA 
 ρdV
 k ∑ qi 



ri 

dq 

 k∫
r

r

r
∂V ˆ ∂V ˆ ∂V ˆ
E=−
i−
j−
k
∂y
∂z
∂x

Capacitancia
C=

Q
∆V

C = εo
1

C eq, par = C1 + C 2 + C 3 + ...

C eq , ser

Circuitos
I=

dq
dt

I=

µ o = 4π × 10
r

r

∫ B ⋅ ds = µ

−7

T⋅m
A

I

o enc

=C = kC o

1
1
1
+
+
+ ...
C1 C 2 C 3

∆V
R

U=

1
Q∆V
2

P = I∆V
1

Req , ser = R1 + R2 + R3 + ...

Campo Magnético

A
dReq , par

=

rr
r
 qv × B 
Fm =  r r 
 Idl × B 
r
ˆ
B = µ o nIu axis

1
1
1
+
+
+ ...
R1 R2 R3

r
τ = µ×B
r

r

rr
Φ B =∫ B ⋅ dA

r
r µ o I dl × u r
ˆ
B=
∫ r2
4π
rr
∫ B ⋅ dA = 0

Campo Electromagnético
rr
dΦ B
fem = ∫ E ⋅ ds = −
dt

rr
dΦ E
B ⋅ ds = µ o Ienc + µ o ε o
∫
dt

Geometría
S circulo = 2πR

Acirculo = πR 2

Asphere = 4πR 2

4
Vsphere = πR 3
3

Φ m = LI

fem = L

dI
dt