/20 /20 /20 /60. Dr. Galeazzi PHY207 Test #3 November 20, I.D. number:

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1 Signature: Name: I.D. number: You must do ALL the problems Each problem is worth 0 points for a total of 60 points. TO GET CREDIT IN PROBLEMS AND 3 YOU MUST SHOW GOOD WORK. CHECK DISCUSSION SECTION ATTENDED: /0 [ ] Dr. Mezincescu 5O, 9:30 10:0 a.m. 3 [ ] Dr. Galeazzi 5P, 11:00 11:50 a.m. [ ] Dr. Zuo 5Q, 1:30 1:0 p.m. TOTAL [ ] Dr. Zuo 5R, :00 :50 p.m. [ ] Dr. Ursino 5S, 3:30 4:0 p.m. [ ] Dr. Ursino 5T, 5:00 5:50 p.m. 1 /0 /0 /60 SEE LAST PAGE FOR EQUATION SHEET 1

2 [1.] This problem has five multiple choice questions (one is on the following page!). Circle the best answer in each case. [1A.] A point particle with charge moves with velocity, with and positive. At time 0 the particle passes through point P of coordinates,,0. Find the magnetic field generated by the particle at the origin at 0. BE CAREFULL WITH THE VECTORS! [a] [b] [c] [d] [e] [1B.] The ring shown in the picture lays on the x-y plane and carries current clockwise. What is the magnetic field generated by the ring at the origin? [a] 0 [b] [c] [d] [e] [1C.] In general, what happens to the permeability of a ferromagnetic material when the temperature increases? [a] Nothing [b] It becomes smaller [c] It becomes bigger [d] Depends on the material [e] It becomes zero [1D.] In an LC circuit as shown below, the charge on the capacitor changes with time as cos. What is the total energy stored in the circuit (L+C) as a function of time? [a] [b] [d] sin [c] sin [e]

3 [1E.] A magnetic field fills the space with x>0. Where C is a constant. A square loop of wire with resistance R and side L is placed with the left side at a distance x from the y- axis (see figure). If the loop is moved to the right with constant speed v, calculate the magnitude and direction of the current flowing through the loop, as a function of the distance x, for x>0. [a] counterclockwise [b] [d] clockwise clockwise [c] [e] 0 counterclockwise 3

4 [.] A toroidal solenoid has inner radius, outer radius, a rectangular section with width, and a wire is coiled times around it (see figure). The core of the solenoid is made of iron, with permeability. a) Use Ampere s Law to DERIVE an expression for the magnitude of the magnetic field inside the solenoid as a function of the distance r from the axis of the torus. b) If the current through the solenoid changes with time, use Faraday s law to DERIVE and expression for the electromotive force induced in the solenoid as a function of the current change. c) From the result in part (b) DERIVE an expression for the self-inductance of the solenoid. Show your work if you want to get points. a) Using a circular path with radius and center on the axis of the torus, // and can depend only on, b) If I choose a sectional area base and height, and with same direction of B, //: Φ Φ Φ ln ln c) ln ln 4

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6 [3.] In the circuit shown below, find: a) The power dissipated in resistor right after the switch S is closed. b) The power dissipated in resistor a long time after the switch S is closed. c) The energy stored in the capacitor a long time after the switch S is closed. d) The energy stored in the inductor a long time after the switch S is closed. MAKE SURE TO JUSTIFY YOUR ANSWERS! a) Right after the switch is closed the solenoid acts as an open circuit and the capacitor as a short circuit. Therefore the capacitor shorts the right side of the circuit, which does not have any current. The circuit therefore reduced to the one shown on the left. b) A long time after the switch is closed, the solenoid acts as a short circuit, the capacitor as an open circuit. The circuit reduces to the one on the left, where is short-circuited and does not do anything. c) The capacitor is connected between points a and b in the figure. Therefore the voltage is 1 1 d) The inductor is connected through points c and d in the figure. Therefore 1 1 6

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8 Some useful relations: (Feel free to detach this page and keep for your own record) Electric Field: Electric Force: Electric Dipole: ; ;. Gauss Law: Electric Potential: ; Energy: ; ; Parallel plates: Capacitors: ; parallel: C... eq C1 C ; series:... C eq C1 C Energy: U 1 QV ; Energy density: u 1 E Dielectrics: K o Resistors: I dq ; R V ; R L dt I A Resistors in series: R eq R1 R...; Resistors in parallel:... R eq R1 R Power: Kirchhoff rules: I 0 - node rule; V 0 - loop rule Magnetic Force: ; ; straight wire in uniform field Magnetic dipole: ; o qv rˆ o Idl rˆ Biot-Savart: B, db 4 4 r r B 1 Magnetic energy: u m, U LI Ampere s law: Faraday s Law: ; Φ Self inductance: ; Mutual inductance: 8