# Quiz4 formulas ```PHYSICS 2B
PROF. HIRSCH
QUIZ 4
WINTER QUARTER 2010
FEBRUARY 8, 2010
Formulas:
sin 30 o = cos 60o = 1 / 2, cos30o = sin60 o = 3 / 2, sin 45o = cos 45o = 2 / 2
r
q1q2
kq1q2 r r
9
2
2
Coulomb's
law
;
k
=
9
×10
N
⋅
m
/C
;
F
r ( r2 − r1 )
12 = r
2
r
| r2 − r1 |3
r kq
r
r
Electric field due to charge q at distance r :
E = 2 rˆ ; Force on charge Q: F = QE
r
2kp
kp
Electric field of dipole: along dipole axis / perpendicular:
E= 3 / E= 3
(p=qd)
€
x
y
r r r r r
€
Energy of and torque on dipole in E-field: U = − p ⋅ E , τ = p × E
F=k
€
€
Linear, surface, volume charge density : €
dq = λ ds , dq = σ dA
2kλ
Electric field of infinite : line of€charge : E =€ ;
r
Gauss law :
€
Φ=
r
r
∫ E ⋅ dA =
qenc
ε0
€
€
€
€
€
€
€
€
€
Φ = electric flux ; k =
1
; ε0 = 8.85 ×10−12 C 2 /Nm 2
4 πε0
B r
→
B →
→
U B − U A = ΔU AB = −W AB = - ∫ F ⋅ dl = - ∫ qE ⋅ dl = qΔVAB = q(VB − VA )
A
€
;
V=
kq
;V=
r
∫
kdq
r
; V=
Electrostatic energy : U = k
A
kpcos θ
(dipole) ;
r2
, dq = ρ dV
€
sheet of charge : E = 2πkσ = σ /(2ε0 )
El = −
∂V
∂l
;
V=N/C
r
r
E = -∇V
q1q2
; Capacitors : Q = CV ; with dielectric : C = κC 0 ; ε0 = 8.85 pF /m
r
2πε0 L
ab
cylindrical ; C = 4 πε0
spherical
ln(b /a)
b−a
Q2 1
1
1
Energy stored in capacitor : U =
= QV = CV 2 ; U = ∫ dv uE ; uE = ε0 E 2
2C 2
2
2
Capacitors in parallel : C = C1 + C2 ; in series : C = C1C2 /(C1 + C2 )
Elementary charge: e = 1.6 ×10 -19 C
r r
r
r
r r
r
r
dq
eEτ
m
l
I=
= ∫ J ⋅ dA ; J = nev d ; v d =
; ρ = 2 ; R = ρ ; E = ρ J , J = σE
dt
m
ne τ
A
−1
V = IR ; P = VI = I 2 R = V 2 /R ; Pemf = εI ; Req = R1 + R2 (series) ; Req
= R1−1 + R2−1 (parallel)
€
Charging capacitor : Q(t) = Cε(1− e−t / RC ) ; Discharging capacitor : Q(t) = Q0e−t / RC
C=
ε0 A
parallel plates ;
d
C=
```