Summary Phys 142 - Midterm exam cheat sheet

Cheat Sheet — Midterm 2
PHYS 142 (Summer 2014)
Constants:

ǫ0 = 8.9 × 10−12 C2 /N · m2 µ0 = 4π × 10−7 Wb/A · m g = 9.8 m/s2
−19 −31
e = 1.6 × 10 C me = 9.1 × 10 kg mp = 1.7 × 10−27 kg

Charges, Currents, and the Electromagnetic Field
Forces on Charges and Currents: Flux:
ˆ ¨ ¨
~ = q( E
F ~ +v ~
~ × B) ~ = Id~l × B
F ~ ΦE = ~ · n̂ dA
E ΦB = ~ · n̂ dA
B
A A

Maxwell’s Equations:

~ · n̂ dA = Qenc ~ · d~l = − dΦB ~ · d~l = µ0 Ienc + µo ǫ0 dΦE
‹ ‹ ˛ ˛
E ~ · n̂ dA = 0
B E B
A ǫ0 A l dt l dt

Sources of Electric and Magnetic Field:

1 q 1 dq ~ = µ0 q~v × r̂ ~ = µ0 Id~l × r̂
ˆ ˆ
~ =
E r̂ ~ =
E r̂ B B
4πǫ0 r2 4πǫ0 r2 4π r2 4π l r2
Electrostatic Potential:
b
1 dq ~ = − ∂V ı̂ − ∂V ̂ − ∂V k̂
ˆ ˆ
V = Va − Vb = ~ · d~l
E ~ = −∇V
E
4πǫ0 r a ∂x ∂y ∂z

Electric Dipoles Magnetic Dipoles:

p = q~d
~ ~
τ~ = ~p × E ~
U = −~p · E ~ = IAn̂
µ ~
~τ = ~µ × B ~
U = −~µ · B

Energy in Fields: Motion in B-Field: B-Fields of Infinite Objects:

1 1 2 mv µ0 I
U = ǫ0 E 2 + B R= B= (wire) B = µ0 nI (soleniod)
2 2µ0 |q|B 2πr

Electrical Circuits
Current: Kirchoff’s Rules: Faraday’s Law:

dQ ~ = nq~v d E X X dΦB
I= = n|q|vd A J ρ= V =0 I=0 E = −N
dt J junction
dt
loop

Capacitors:
n n
Q 1 1 1 Q2
U = CV 2 =
X X
C= = (Series) Ceq = Ci (Parallel)
V Ceq C 2 2C
i=1 i i=1