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1 Physics: Dr. F. Wilhelm E:\Excel files\3 lecture\3 tests\final 3 F7 Practice.doc page 1 of 9 NAME:... POINTS:... Dr. Fritz Wilhelm, Diablo Valley College, Physics Department Phone: (95) Extension: 43 Midterm 1 physics 3, chapters May 13, 8 NOTE: TO ENSURE FULL CREDIT EMPHASIZE YOUR ANSWERS AND INCLUDE DIMENSIONS. SPECIFY WHICH PRINCIPLES OR LAWS YOU ARE USING. EXPLAIN RIEFLY WHAT YOU ARE TRYING TO DO. ORGANIZE YOUR WORK LOGICALLY. USE DRAWINGS! Use the correct number of significant figures. USE scientific notation for numbers larger than 1 and smaller than 1/1. Unless otherwise specified, do not use more than 3 significant figures. 1. [1] A circular polarized electromagnetic wave propagates in the x-direction with a wavelength of 1. cm. The amplitude of the electric field is 1V/m. At a time when the magnetic field points in the +z direction, what is the direction of the electric field? Make a drawing with the correct directions for E and fields. Find the angular frequency and the wavenumber.

2 Physics: Dr. F. Wilhelm E:\Excel files\3 lecture\3 tests\final 3 F7 Practice.doc page of 9. [1] The capacitor of a RLC circuit is first charged to a maximum charge of 15. μc, then the emf is being removed. R45 Ohms, L5.mH, C8mF. Write down the differential equation for the charge in this circuit. Find the resoncance angular frequency at which the charge oscillates in the circuit. Compare this to the oscillation of the spring with damping. Write down the total energy of the circuit and show that it loses power according to RI. 3. [1] Use Ampere s law to calculate the magnetic field inside of a toroid with 85 turns. The inner radius of the rectangular coils is 3. cm, the outer radius is 7. cm. The current in the coil is.5a. The current is 1.58A

3 Physics: Dr. F. Wilhelm E:\Excel files\3 lecture\3 tests\final 3 F7 Practice.doc page 3 of 9 4. [1] Calculate the change in entropy of 5g of water, heated slowly from to 8ºC. (Note that dqmcdt) 5. [1] Find the density of oxygen gas at a pressure of 1.atm and a temperature of 5.ºC.

4 Physics: Dr. F. Wilhelm E:\Excel files\3 lecture\3 tests\final 3 F7 Practice.doc page 4 of 9 6. [1] The rotating coil with 8 loops in an ac generator has a radius of 1.5m. It is rotated at 6.Hz in a uniform field of.8t. a) Calculate the flux through the loop as a function of time, and the emf induced in the loop. 7. [1] An RLC (in series) circuit is driven by an ac voltage with V max 1V. R1. Ohms, L5.mH, C1μF, ω1/s. Find the maximum current in the circuit and the phase change with respect to the voltage. Find the rms current. Use complex impedances. Calculate the resonance frequency of this circuit. Find the maximum power of the circuit. Calculate the voltage across the capacitor.

5 Physics: Dr. F. Wilhelm E:\Excel files\3 lecture\3 tests\final 3 F7 Practice.doc page 5 of 9 ik ( ir ωt) For vector fields of the form A e we can simplify the rules of derivation as seen in class: 8. [1] iω t ik Show that the direction of propagation is perpendicular to both the electric field vector and the magnetic field vector. (Use dive and div ) Apply all this to Faraday s law and prove that Ec.

6 Physics: Dr. F. Wilhelm E:\Excel files\3 lecture\3 tests\final 3 F7 Practice.doc page 6 of 9 9. [1] Calculate the capacitance of a coaxial cable with inner radius a and outer radius b. Start with Gauss s law to calculate the electric field inside of the capacitor. Then calculate the potential difference between the two cylinders, which you may consider to be infinitely thin. Make a drawing and show the Gaussian surface and the electric field lines In SI units the magnetic field in an em wave is described as y 1 sin ( 1 x ωt) Find the amplitude of the corresponding electric field oscillations, wavelength and frequency. 11. Show that the electric potential V of a static electric charge q obeys the differential ρ equation: Δ V In a region of space where there are no charges, the right side of this ε equation is.

7 Physics: Dr. F. Wilhelm E:\Excel files\3 lecture\3 tests\final 3 F7 Practice.doc page 7 of 9 Formulas: h k R J mole K Latm mole K π Js AΔT σ ( Stefan); Q eaσt ; Δ U ncvδt ; CP CV R; mv kt; Q Li k ; /.86 / ; ; f γ 1 γ dqr const;pv ; const; Δ + ; Δ ; λ 1/ π V T i TV Nk T nrt PV U Q W S d n E V f kt nde n e de; W PdV;1cal J; Lwater 8 cal / g Vi 1 σ ε A ke ; ε S. I. ;parallel plate capacitor: E ; C κ 4πε d 9 1 ε b Q 1 Q 1 Q 1 E ; E grad V; Δ V E ds; C ; F qe; U C ΔV r V C ab 4πε Δ a ( ) t RC dw qdv; Udipole pie; τ p E; q Cε 1 e ; mp 1.67E 7kg 938 MeV / c b 1 Δρ coaxial : C L /ke ln ; I Q jda; j nqv d; j σe; ρω ; αδt a σ ρ surface copper ρ Ω m at C α C Δ V RI P IΔ V RI Δ V ε ri 8 5 : Ω ; / ; ; ; (1.1) ρ dive ;(1.) F qv ε (1.3) df I ( ds ) (1.4) μ IA magnetic dipole moment (1.5) U μ ; τ μ (1.6) curl μ j μi ds r μi ds u (1.7) d r μ ;iot-savart ; 1 ; μ π r 4π r 4π E (1.8) curl μ j + ε displacement current t j d dφ (1.9) Faraday s law E ε N t dt 7 6 ; i

8 Physics: Dr. F. Wilhelm E:\Excel files\3 lecture\3 tests\final 3 F7 Practice.doc page 8 of 9 d d d A Acos dt dt dt Acos t Aωsin ω t dφ di (1.11) ε L N L dt dt NΦ (1.1) L I 1 (1.13) U LI electromagnetic energy in an inductor Energy (instantaneous) density in a capacitor and coil: 1 (1.14) ue ε E ; u μ ac currents Vt ˆ( ) Imax Vmax It ˆ( ) ; Irms ; Vrms zˆ (1.1) ε ( ) ( θ) ( ω ) eq max (1.15) ˆ Vt ˆ( ) V ZL iωl Iˆ() t ; Imax iωl ωl ˆ 1 Z ˆ() ˆ C It iωcvt (); Imax ωcv iωc (1.16) P Vˆ Iˆ cos Φ rms rms 1 1 (1.17) I n electromagnetic fields: E c; ue () t ε E ; u () t μ Instantaneous energy density in an em wave with equal contributions from (1.18) u() t the electric field and the magnetic field: total ε E μ 1 max ε uavg Emax μ Poynting vector, averaged over a period (1.19) 1 Emax 1 cmax S avg ; με c 1 μ c μ max 1 c ; εμ S U Fdx (1.) u pressure P in an em-wave c V Adx U (1.1) momentum of e.m. wave p Perfect reflector c U (1.) momentum of e.m. wave p Perfect absorber c

9 Physics: Dr. F. Wilhelm E:\Excel files\3 lecture\3 tests\final 3 F7 Practice.doc page 9 of 9 A ( C) A C C A for any three vectors A,, C (1.3) ( i ) ( i ) ikr ( i ωt) Exyzt (,,, ) E Ee (1.4) ik ( ir ωt) xyzt (,,, ) e ( iωt) iω t ik (1.5) curl ik ; div ik U gradu iku Δ i Laplace ik k ( )

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