# Emf b l v sin θ or when flux changes through a loop

• apoorpremed200
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emf = B L v sinθor when flux changes through a loop of wire: emf = - φ/∆t Right Hand Rule: FirstFinger=Field seCond=Current Vum=Vel of wireLenz's Law:induced emf produces a current whose B field opposes the change in magnetic flux through a current loop thus creating a repulsive force (no free lunch) IV.WAVES AND OPTICS15% A.1. Properties of traveling waves Wave motion a) V = f λ[Hz = cycle / second = wave / second] period (T) =1/frequency b) displacement: x = A cos (ωt); ω= 2πf [ωis angular velocity] c) wave is inverted when reflected from fixed end. Reflects from free end upright. 2. Doppler effect. frequency shift with relative motion f, = f (v ±vo) / (v ±vs3. Superpositionadd individual waves point by point )(s: source, o: observer) choose signs so that frequency shifts higher for converging object and source, shifts lower for diverging. a) constructive interference (increased amplitude - may be. bright) b) destructive interference (decreased amplitude. may be node) c) fbeat= ~f1–f24.Properties of standing waves; resonance [two identical waves passing through each other] ~beats (beat frequency gives difference in f between two tones) a) natural frequencies of vibration: ffunb) string: v = (T / [m / L] )T: Tension m: mass of string L: Length of string. , 1st overtone, 2nd overtone, 3rd overtone Node at fixed end; Antinode at loose end. c) pipes; Antinode at open end, node at closed end. B.1. Interference and diffractionPhysical Opticssingle slit interference: n λ= a sinθ(nλis path difference) max at n = 0, 1.5, 2.5, 3.5, 4.5 min at n = 1, 2, 3 smooth transition between max and min. W-i-d-e central max. a is width of single slit. double slit interference: n λ= a sinθ(nλis path difference) max at n = 0, 1, 2, 3, 4 min at n =0.5, 1.5, 2.5, 3.5 smooth transition between max and min. a = distance between centers of slits. multiple slit interference(diffraction grating): nλ= a sinθsame as double slit , a is distance between adjacent slits min is everywhere except at exactly at max. 2. Thin film interference(a) 180°phase change (flip) when reflect off higher refractive index (out of phase) (b) no phase change when reflects off lower refractive index (in phase) (c) don't forget λchanges within medium. 3. Dispersion of light and the electromagnetic spectrum. (a) EM radiation = transverse wave (of E field and B fields at right angles) (b) low frequencies (long wavelengths ~ red end of spectrum) diffract and refract (bend) less than high frequencies (short wavelengths ~ blue end of spectrum) (c) EM spectrum: (from short to long wavelengths): cosmic. gamma, x ray, ultraviolet. Visible (blue to red), infrared, microwave. radiowaves C.1. Reflection and refraction Geometric opticsa)law of reflection: angle of incidence = angle of reflection(easy!) a) Snells law: ni sin i = nrb) If nsin r(n = c/v) i> nrc) If nlight bends away from normal i< nre) sin Clight bends toward normal = n2/n1light can only be totally internally reflected if the light is passing from more dense to less dense (n1> n2f) Light decreases wavelength, but keeps the same frequency, when passing from less dense to more dense.
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