8.02
Final Physics Exam: Equation Sheet
Fall 2006
Some (possibly useful) Relations: Force Laws: Current:
F = q(Eext + v Bext )
J = v
dF = I d s Bext
I=
open surface
J da
1 dq ^ Source equations: dE = 4 r 2 r o dB =
B=
^ o q v r 2 4 r
v << c
^ o I d s r 2 4 r
^ r points from source to observer
Qinside
Maxwell's Equations:
closed surface
E da =
o
closed surface
B da = 0
= - dB
dt
contour
B dr =o I through + o 0
d E da dt open
surface
Electromotive Force:
= ( E + v B ) dr
open surface
Magnetic and Electric Flux: B
B da
E
open surface
E da
Electric Potential Difference:
Vmoving from a to b = Vb - Va = - E dr
a
b
Vmany point charges =
i =1
N
qi 4 o r - ri 1 Q2 1 = C V 2 2 C 2 V 2 = i V = i R = R
2
Capacitance:
C=
Q V
U=
Resistance:
V = IR
Pohmic heating
Inductance:
L=
N B,self,sgl coil I
back
= -L
dI dt
U L = 1 LI 2 2
1 2 Energy Stored in Fields: uE = 2 0 E
1 S = EB Energy Flow: = 0
Ppower S da
uB =
B2 2 o
AC circuits: 0 = LC
1
X L = L
X C = 1/ C
2
XR = R
tan = X / R
Series RLC : Z = R 2 + X 2 = R 2 + ( X L - X c ) Magnetic Dipoles:
=I A n
V0 = I 0 Z
n perpendicular to loop, right-handed with respect to I
= B
Fz = z
dBz dz
Waves:
c=
1 00
f =1 T
= 2f
k = 2
c = T = f = k
Interference and Diffraction:
Double Slit: Constructive: d sin = m, m = 0, 1, 2, 3, ...
1 Destructive: d sin = m + , m = 0, 1, 2, 3, ... 2
Single Slit: Destructive: a sin = n , n = 1, 2, 3, ... Some potentially useful numbers
o = 4 10-7 T m A -1
c = 3 108 m s -1
ke =
1 4 0
= 9 109 N m 2 C-2
e = 1.6 10-19 C
8.02 Final Exam Fall 2006
FAMILY (last) NAME
GIVEN (first) NAME
Student ID Number Your Section: ___L01 MW 10 am ____L02 MW 12 pm
Your Group (e.g. 10A): ______________
Problem
Score
Grader
Part 1 (30 points) Problem 1 (15 points) Problem 2 (20 points) Problem 3 (20 points) Problem 4 (15 points)
TOTAL