8.02
Exam Physics Three Please Remove this Tear Sheet from Your Exam
Fall 2007
Some (possibly useful) Relations: 1 dq ^ dE = r 4 o r 2 Qfree, inside E dA =
closedsurface
o
dA points from inside to outside
A Q Cparallelplate = o d V 2 1 U = C V 2 = Q 2C 2 = RC X C = 1 C
C=
L= B,self,total I
E ds = - dt B dA
d
=-
b
d total dt
back = - L
dI dt
Vmoving from a to b = Vb - Va = - E d s
a
U L = 1 LI 2 2
^ q vr B= o 2 4 r
^ I ds r v << c dB = o 2 4 r
= L/R
X L = L
Z = R2 + X 2 = R2 + ( X L - X C ) tan = X R
k = 2
- 12
2
^ where r points from source to observer
Series RLC:
closed surface
B dA = 0
= 2f = 2 T
dE B d s =o I through + 0 dt contour where Ithrough is the current flowing through any open surface bounded by the contour: I through = J dA
c = = T f = k = ( 0 0 ) ^ ^ ^ E0 = vlight B0 EB = p
S=
1 EB 0
Pabsorb =
S 2S ; Preflect = c c
open surface
ds is right-handed with respect to dA 1 B2 uE = 0 E 2 uB = 2 2o
F = q E + v B ext
If the function D(t ) satisfies the equation d D(t ) D(t ) = - , then D(t ) = Do e -t / dt
Cross-products of unit vectors:
^^ = ^^ = k k = 0 i i j j ^ ^ ^^ = k ^k = ^ k ^ = ^ i j ^ j ^ i ^ i j
(
)
dF = I d s B ext
Fcent. = mv 2 r
= IA n
= B
V = IR
Fz = z R=
2
dBz dz
L
A
Pohmic heating
V 2 = I V = I R = R
Some potentially useful numbers 1 N m2 Tm ke = = 9 109 o = 4 10-7 2 4 0 C A 6 Breakdown of air E ~ 3 x 10 V/m Earth's B Field B ~ 5 x 10-5 T = 0.5 Gauss Speed of light c = 3 x 108 m/s Light (blue to red) = 400 nm to 700 nm Electron charge e = 1.6 x 10-19 C Avogadro's number NA = 6.02 x 1023 mol-1