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43 Cards in this Set
- Front
- Back
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Gauss' Law for Magnetic fields |
∫ B · dA = 0
(no magnetic monopoles) |
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Maxwell and Ampere, induction |
∫ B · ds = µ₀i_d,enc + µ₀i_enc
induced E flux and enclosed current are related to B by the fundamental constants |
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Displacement current |
i_d = ε₀ · d∅_e/dt Fictitious current due to changing electric field |
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Gauss for Electricity |
∫ E·dA = q_enc / ε₀
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Faraday's Law of induction |
∫ E · ds = - d∅_b / dt
Magnetic flux related to e field |
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Energy in a magnetic dipole |
U = - µ · B |
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Magnetization |
M = C * B_ext/T T = temperature C= curie constant |
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Ferromagnetic material |
Magnetic moment can be aligned by external field.
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Paramagnetic material |
Attracted to region of stronger magnetic field when placed in one. |
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Diamagnetism |
Diamagnetic materials exhibit magnetism only when placed in an external magnetic field; there they form magnetic dipoles directed opposite the external field. |
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Instantaneous E (wave) |
E = E_m sin(kx - omega*t) B = B_m sin(kx - omega*t) |
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c , speed of light |
1 / √ ( µ₀ε₀) |
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Energy transport, EM wave |
Poiynting vector S = 1 / µ₀ ( E × B) |
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Intensity |
I = Erms ² * 1 / (c µ₀) |
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Loop Rule |
Any voltage drop across any loop must equal the voltage drop across any other loop |
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Junction rule |
Current in = current out |
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Radiation force |
F = IA/ c [total absorption] F = 2IA / c [total reflection along a path] |
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Radiation pressure |
p = Intensity / c |
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For initially un-polarized light, what is the change in intensity? |
I = I₀* 0.5 |
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For initially polarized light, what is the change in intensity? |
I = I₀ cos²(θ) |
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Snell's law of refraction |
n1 sinθ1 = n2 sinθ2 |
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Total internal reflection occurs at the critical angle: |
θc = sin⁻¹ (n2/n1)
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Total polarization occurs by reflection at the angle: |
θB = tan⁻¹(n2/n1)
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Thin lens (also works for spherical mirror) |
1 / o + 1 / i = 1/ f = 2/ r f = focal length r = radius of curvature |
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Spherical refracting surface |
n2 - n1 / r |
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Lateral magnification |
m = - i / o |
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Magnifying lens, angular magnification |
mθ= 25cm / f f = focal length |
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Overall magnification |
M = mmθ |
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Refracting telescope, angular magnification
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m_θ = - f_ob / f_eye |
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Wavelength of light, in a medium |
λ_n = λ / n
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Double slit interference, maxima and minima |
dsinθ = mλ maxima dsinθ = (m + 1/2)λ minima d = slit separation |
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Coherent light |
If two light waves that meet at a point are to interfere perceptibly, the phase difference between them must remain constant with time; that is, the waves must be coherent. |
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Resultant intensity of two interfering waves |
I = 4 I₀cos²(1/2 phi) phi = 2πd / λ · sinθ |
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Thin film interference |
2L = (m + 1/2) · λ/n2 maxima 2L = (m λ / n2) minima |
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Diffraction (single slit) |
asinθ = mλ Location of minima |
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Intensity at any given θ (single slit) |
I= I_m (sinα / α)² α = πa/λ sin θ |
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Circular aperture |
sinθ = 1.22 λ/d |
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θ_R (limit of being resolved)
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1.22 λ/d |
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Double slit intensity |
I = I_m cos²β (sinα/α)² β=πd/λ sinθ |
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Half width angle |
θ_hw = λ / Ndcosθ
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Dispersion |
m / dcosθ |
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Resolving power |
R = λ_avg / ∆λ
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Bragg's law |
2dsinθ = mλ |
