Currents and circuits
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Current: |
I = ∆Qnet/∆t
= ∫j∙dA, j = current density |
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Resistance: |
R = ∆V/I |
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Resistance of a straight wire: |
R = ρL/A |
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Power: |
P = I∆V = I2R = (∆V)2/R |
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Resistors in series: |
R = R1
+ R2 + R3 |
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Parallel Resistors: |
1/R = (1/R1)
+ (1/R2) + (1/R3) |
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RC circuits time constant: |
τ = RC |
Magnetostatics
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Magnetic force on a moving charge: |
F = qv × B |
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Magnetic force on a long straight wire: |
F = IL × B |
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Charged particle in a magnetic field: |
r = mv/(qB) |
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Ampere's law: |
∮Γ B∙ds = μ0Ithrough Γ |
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The magnetic field of a long straight wire: |
B = μ0I/(2πr) |
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The magnetic field inside a solenoid: |
B = μ0nI |
Current loops
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Magnetic moment: |
μ = IAn |
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Torque: |
τ = μ × B, τ = μB sinθ |
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Potential energy: |
Uμ = -μB cosθ |
Faraday's Law
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Faraday's law:
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Induced emf = ∫around loopE·dr =
-∂ΦB/∂t (through a fixed area) |
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Magnetic flux: |
ΦB = ∫AB·dA, dΦB
= B dA cosθ, |
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Induced current: |
I = emf/R |
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Transformer:
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V2/N2
= V1/N1, V2 I2 ≤ V1
I1 |
Electromagnetic Waves
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Energy density in EM fields: |
u = ½ε0E2 + B2/(2μ0) |
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Energy flux S, intensity I: |
S = (1/μ0)E ×
B, I is
proportional to Emax2 |
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Sinusoidal waves: |
E(x,t) = Emaxsin(kx - ωt + φ), Brad
= Erad/c |
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Polarizers: |
Itransmitted = I0cos2θ. |
Geometrical Optics
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Law of reflection: |
θ1 = θ2 |
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Law of refraction: |
n1sinθ1 = n2sinθ2 |
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Total internal reflection: |
sinθc = n2/n1 |
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Mirror equation: |
1/xo + 1/xi = 1/f, M = -xi/xo,
f = R/2 |
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Lens equation: |
1/xo + 1/xi = 1/f, M =- xi/xo |
Wave Optics |
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Double slit, diffraction grating (maxima): |
d sinθ = mλ, m = 0, 1, 2, ... |
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Single slit (minima): |
w sinθ = mλ, m = 1, 2, ... |
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Resolving power: |
θmin = 1.22 λ/D |
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Constructive interference (thin oil film on water): |
2noiltcosθt =
(m+1/2)λ, m = 0,1,2,… |