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Unformatted text preview: zes the crucial equations regarding orbits. Note that
since E and L are conservedquantities for the orbit, we can calculate these
quantities using position and velocity information at any point on the orbit.
Applying theseequati6nsallows us to solve an astonishingvariety of interestingo rbit p roblems.E xamples l3.L t hrough N 13.4a rej ust a s ample.
N We c arr r .rsc l.rt' cluationsi n
tc
tablc Nl3. I to solvea vtrricty
of orbit prolrlenrs Winter Quarter 2014
122B (honors) Exam 3 Equations speed of light c = 3.00 × 108 m / s me = 9.11 × 10−31 kg e = 1.602 × 10 −19 m p = 1.67 × 10−27 kg
18 C, 1 C = 6.24 × 10 e qq
1 q1q2
ˆ
ˆ
F (r) =
r = k 1 2 2 r ε0 = 8.85×1012 farad/m. k = 8.99×109 Nm2/C2
4πε0 r 2
r F = qE 1q
q
ˆ
ˆ
E (r) =
r=k 2r
4πε0 r 2
r τ = pe × E , pe = qd 1
w = ε0 E 2
2 12
B’
energy density in magnetic field w =
2µ 0
energy density in electric field The distance from earth to moon is 3.8×105 km. The mass of the moon is 7×1022 kg. The mass of the
earth is 6×1024 kg. The radius of the moon is 1,700 km.
Avogadro’s number (a mole) is 6.02×1023. A mole of protons weighs about a gram.
The speed of light is 3.×108 m/s.
Electric field between oppositelycharged parallel plates E = σ / ε0
Work to move charge through electric potential W = qΔV (the textbook calls it W = qΔφ ) 1q
q
=k
4πε0 r
r ∂V
dV = − E • dr E x = −
∂x Q = C ΔV Parallel plate capacitor C = ε 0 A / d
V (r) = J =σE dq I=
= JA = ρ vd A = nqAvd
dt
V = IR P = IV = I 2 R = V 2 / R
For a wire R = L / (σ A ) Series resistors R = R1 + R2 + … , parallel resistors 1 R = 1 R + 1 R + …
1
2 F = qv × B = IL × B P⊥
qB τ = µ × B µ = NAI µ dl × r
ˆ
dB = 0 I 2 4π
r
∂
∂
∂
∇ • E = E x + E y + E z = ρ / ε0 ∂x
∂y
∂z
∂
∂
∂
∇ • B = Bx + By + Bz = 0 ∂x
∂y
∂z #∂
∂ & #∂
∂ & #∂
∂&
ˆ
ˆ
ˆ
∇ × B = x % Bz − By ( + y % Bx − Bz ( + z % By − Bx ( = µ0 J statics only ∂z ' $ ∂z
∂x ' $ ∂x
∂y '
$ ∂y ˆ
∫ A • n dA = ∫ τ ∇ • A d τ Divergence theorem: S is a sur...
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This document was uploaded on 03/08/2014 for the course PHYS 122 at University of Washington.
 Spring '08
 cramer
 Magnetism

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