Phys 132 Equation Sheet Fall 2005
Electric Forces and Fields: ~
E=1
4π0
q
r2ˆr~
F0=q0~
E~
E=1
4π0X
i
qi
r2
i
ˆri
ΦE=I~
E·d~
AΦE=Qin
0
~τ =~p×~
E U =−~p·~
EInfinite sheet: E=η
20
Electric Potential: V=1
4π0
q
rU=q0V V =1
4π0X
i
qi
ri
V=1
4π0Zdq
r
Vf−Vi=−Zf
i
~
E·d~s Es=−dV
ds ~
E=−∇V=−ˆ
i∂V
∂x +ˆ
j∂V
∂y +ˆ
k∂V
∂z
Capacitance: C=Q
∆Vc
C=0A
d
1
Cseries
=1
C1
+1
C2
+1
C3
+···
Cparallel =C1+C2+C3+·· · U=1
2QV u =1
20E2=K0
Circuits: I=dQ
dt ∆V=IR P =I(∆V)Rseries =R1+R2+R3+···
1
Rparallel
=1
R1
+1
R2
+1
R3
+··· τ=RC q =Q0e−t/τ
Magnetic Forces and Fields: ~
F=q~v ×~
B d ~
F=Id~
l×~
B ~τ =~µ×~
B U =−~µ ·~
B
µ0Iencl =I~
B·d~s d ~
B=µ0
4π
Id~
l׈r
r2Long straight wire: B=µ0I
2πr
Center of current loop: B=µ0I
2rLong solenoid: B=µ0nI
Induction: ΦB=Z~
B·d~
A ε =−dΦB
dt ∆VL=−Ldi
dt UL=1
2LI2uB=B2
2µ0
τ=L/R ω =1
√LC I~
E·d~
l=−dΦB
dt I~
B·d~
l=µ0ic+0
dΦE
dt encl
Electromagnetic Waves: ~
F=q(~
E+~v ×~
B)vem =c= 1/√0µ0
E(x, t) = ˆ
jEmax sin(kx −ωt)B(x, t) = ˆ
kBmax sin(kx −ωt)k=2π
λω= 2πf
c=λf E =cB ~
S=1
µ0
(~
E×~
B)I=I0cos2θ
AC Circuits: v(t) = Vcos(ωt +φ)Vrms =V /√2XC= 1/ωC XL=ωL
Z=qR2+ (XL−XC)2Pave =Vrms Irms cos φ
Kinematics: v=v0+at x =x0+v0t+1
2at2v2=v2
0+2a(x−x0)ar ad =v2
r
Vectors: Ax=Acos θ Ay=Asin θ A =qa2
x+A2
y~
A·~
B=AB cos φAB
~
A·~
B=AxBx+AyBy+AzBz~
A×~
B= ˆnAB sin φAB
Math: ax2+bx +c= 0 x=−b±√b2−4ac
2a(1 + x)n≈1 + nx for x1
Constants: e= 1.602 ×10−19 C0= 8.85 ×10−12 C2/Nm2
µ0= 4π×10−7N/A2me= 9.109 ×10−31 kg c= 3.00 ×108m/s
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