PHY2061 Exam 3: RLC Circuits and Electromagnetic Waves - Prof. Darin E. Acosta, Exams of Physics

Download PHY2061 Exam 3: RLC Circuits and Electromagnetic Waves - Prof. Darin E. Acosta and more Exams Physics in PDF only on Docsity! Page 1 of 10 PHY2061 12-11-06 Name:_______________________ ___ Exam 3 Closed book exam. A calculator is allowed, as is one 8.5×11” sheet of paper with your own written notes. Please show all work leading to your answer to receive full credit. Numerical answers should be calculated to at least 2 significant digits. Exam is worth 100 points, 25% of your total grade. UF Honor Code: “On my honor, I have neither given nor received unauthorized aid in doing this exam.” Sphere: 2 344 3.1415927 3 S r V rπ π π= = = e = × −16022 10 19. C 29.8 m/sg = 61 C 10 Cμ −= 61 F 10 Fμ −= 121 pF 10 F−= 191 eV 1.6 10 J−= × 9 2 2 0 1 9 10 N m / C 4 K πε = = × 12 2 20 8.8542 10 C / N mε −= × c = ×30 108. m/s 70 2 10 T m / A4 Kk c μ π −= = = ⋅ 60 4 1.257 10 T m /Akμ π −= = × ⋅ 0 0 2 1 c μ ε = 1 2 122 ˆq qK r =F r 0q = FE enc 0 E S qd ε Φ = ⋅ =∫ Ε Α 0 ρ ε ∇ ⋅ =E V= −∇E 0 UV q = C W U d= −Δ = ⋅∫ F s CV dΔ = − ⋅∫ E s C qV C Δ = L diV L dt Δ = dqi dt = eff 1 2C C C= + eff 1 2 1 1 1 C C C = + LR A ρ= RC RCτ = LR L R τ = eff 1 2R R R= + eff 1 2 1 1 1 R R R = + V iRΔ = 2 2 VP Vi i R R = = = 2 2 QU C = 21 2 U Li= 12 f LC ω π= = F E v B= + ×q( ) i=F L×B 0 3 4 i dd r μ π = s×rB 0 encC d iμ⋅ =∫ B s 0 wire 2 iB r μ π = 0 4arc iB R μ π = Φ =τ r×F Ni=μ A =τ μ×B U = − ⋅μ B zz z dBF dz μ= B S dΦ = ⋅∫ B Α B dN dt ε Φ= − BL N i Φ = 2 2 0 02 2 E B u ε μ = + Page 2 of 10 PHY2061 12-11-06 Name:_______________________ ___ LR L R τ = 1LC LC ω = tan L CX X R φ −= ( )22 m m L C i R X X ε = + − LX Lω= 1 CX Cω = sinm tε ε ω= ( )sinmi i tω φ= − 0 1 μ = ×S E B av PI S A = = 20 cosI I θ= 1 1 2 2sin sinn nθ θ= 2 fω π= 2k π λ = f vλ = n cv n = sin m d λθ = 2 0 cosI I θ= enc 0 E S qd ε Φ = ⋅ =∫ E A 0B S dΦ = ⋅ =∫ B A C Sd dt ∂ ⋅ = − ⋅ ∂∫ ∫E s B A 0 0 0 0 0 0 E enc encC S d dd i i d dt dt μ μ ε μ μ εΦ⋅ = + = + ⋅∫ ∫B s E A 0 ρ ε ∇ ⋅ =E 0∇⋅ =B t ∂ ∇× = − ∂ BE 0 0 0t μ ε μ∂∇× = + ∂ EB j ( ) ˆ ˆ ˆcurl y yx xz z F FF FF F y z x z x y ∂ ∂⎛ ⎞ ⎛ ⎞∂ ∂∂ ∂⎛ ⎞∇× ≡ = − − − + −⎜ ⎟ ⎜ ⎟⎜ ⎟∂ ∂ ∂ ∂ ∂ ∂⎝ ⎠⎝ ⎠ ⎝ ⎠ F F x y z div yx z EE E x y z ∂∂ ∂ ∇ ⋅ ≡ = + + ∂ ∂ ∂ E E ˆ ˆ ˆ x y z ∂ ∂ ∂ ∇ = + + ∂ ∂ ∂ x y z x x y y z za b a b a b⋅ = + +a b ( ) ( ) ( )y z z y x z z x x y y xa b a b a b a b a b a b× = − − − + −a b x y z sin cos 2 πα α⎛ ⎞= −⎜ ⎟ ⎝ ⎠ cos sin 2 πα α⎛ ⎞= − −⎜ ⎟ ⎝ ⎠ Page 5 of 10 PHY2061 12-11-06 Name:_______________________ ___ 3. [8 points] In a certain region of space there are no magnetic fields present. An electric field does exist, however. If the y-component of the electric field is y mE E x= , where Em is a constant, what is the x-component of the electric field? 4. [8 points] The electric field between the plates of a parallel-plate capacitor whose plates have a large circular radius R is given by sinmE E tω= . What is the magnitude of the magnetic field between the plates of the capacitor a distance r<R from the center? Page 6 of 10 PHY2061 12-11-06 Name:_______________________ ___ 5. The magnetic field of a plane electromagnetic wave propagating in vacuum is described by ( ) ˆsinmB kx tω= +B z in SI units. (a) [4 points] In what direction does the electromagnetic wave propagate? (b) [6 points] Determine the expression for the electric field without introducing any new parameters. (c) [4 points] If 15 -14 10 sω = × what is the wavelength of the electromagnetic wave? Page 7 of 10 PHY2061 12-11-06 Name:_______________________ ___ 6. [8 points] Sunlight reaching Earth has an average intensity of 1.2 kW/m2. Calculate the maximum strength of the electric field assuming the sunlight is a plane wave. 7. [8 points] An unpolarized beam of light is sent into a stack of 4 polarizing sheets, oriented so that the angle between the polarizing directions of adjacent sheets is 30°. What fraction of the incident intensity is transmitted by the system?