(c) In the process of part (b), must energy be supplied to the electron, or is energy released?

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Joella Martin
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1 (1) A capacitor, as shown, has plates of dimensions 10a by 10a, and plate separation a. The field inside is uniform, and has magnitude 120 N/C. The constant a equals 4.5 cm. (a) What amount of charge is stored on the plate on the right? Is it positive or negative? (b) A and B are two points at opposite corners of the capacitor, as shown. What is the change in energy for the process of moving an electron from point A to point B? (c) In the process of part (b), must energy be supplied to the electron, or is energy released? (2) Choose the incorrect statement: (a) A laser beam is composed of electromagnetic waves. (b) As the wavelength of a radio wave increases, its peak electric field always increases. (c) A transformer works for AC currents, but not for DC currents. (d) Inductors have stored energy proportional to the square of the current flowing in them. (e) Curved mirrors can produce both real and virtual images. (3) What is the effective resistance? (choose one): (i) 1 Ω (vii) 4 Ω (ii) 1.5 Ω (viii) 5 Ω (iii) 2 Ω (ix) 7 Ω (iv) 2.5 Ω (x) 9 Ω (v) 3 Ω (vi) 3.5 Ω 2

2 (4) A circuit is connected as shown, with V B = 20 V, R = 15 Ω, and C = 35 µf, and allowed to come to steady-state. The lower right point is ground (consider this zero volts). (a) Find the current in the resistor R. (b) Find the charge on the capacitor. (c) Find the voltage at point A, relative to ground. Is it positive or negative? (d) Later (after steady state was already reached), the switch is opened (new figure). How much time is required for the current in the 4R resistor to reach 1/5 of its initial value? (5) Shown is a thin, hollow, circular hoop, uniformly charged, with total charge +Q covering its circumference. The hoop radius is R. (a) The electric potential at the center of the hoop (point x ), relative to infinity, is (choose one): (i) zero. (vi) kq/(2r). (ii) kq/r. (vii) kq/(2r). (iii) kq/r. (iv) 2#kQ/R. (v) 4#kQ/(3R). 3

(Problem 5 continued from last page) (b) For the same hoop the electric field at the center of the hoop is (choose one): (i) zero. (vi) kq/(2r 2 ). (ii) kq/r 2. (vii) kq/(2r 2 ). (iii) kq/r 2.

3 (Problem 5 continued from last page) (b) For the same hoop the electric field at the center of the hoop is (choose one): (i) zero. (vi) kq/(2r 2 ). (ii) kq/r 2. (vii) kq/(2r 2 ). (iii) kq/r 2. (v) 4#kQ/(3R 2 ). (iv) 2#kQ/R 2. (6) A heating element is composed of wire with cross-sectional area cm 2, and resistivity Ω m. (a) What is the wire resistance, for a 1.5 m length? (b) What current is needed to produce 350 W of heating power, for the 1.5 m wire? (7) A spherical metal shell is shown in cross-section, with a hollow region at its center. The shell has a total, net charge of +2Q (with Q a constant). No other charges are anywhere nearby. (a) What added charge must be placed at the center of the hollow region in order that zero charge appears on the outer surface of the shell? (choose one) (i) 4Q (vi) Q (ii) 3Q (vii) 2Q (iii) 2Q (viii) 3Q (iv) Q (ix) 4Q (v) zero (b) In the case described in part (a), what will be the net flux through an imaginary sphere that completely surrounds the metal shell? (c) Will the potential measured at the outer edge of the metal shell in this case be greater, equal, or less, than the potential at infinity? (d) Will the potential measured at the inner edge of the metal shell in this case be greater, equal, or less, than the potential measured at the outer edge? 4

4 (8) Total internal reflection refers to the situation where (choose the correct statement): (a) for transparent dielectric surfaces there is a maximum wavelength of light beyond which all (b) for light going from high to low index materials there is a maximum angle beyond which all (c) with sufficient silver-coating, an interface between glass and air will reflect all light. (d) a half-silvered mirror will reflect all light that hits it if the region behind it is dark (oneway mirror). (e) for light going from low to high index materials there is a maximum angle beyond which all (9) A very long coaxial cable has currents I 2 and I 1 in the outer and inner conductors as shown, in opposite directions. The inner wire is very thin. The outer conductor is circular in cross section, with inner and outer radius R a and R b, respectively. (a) Find the magnetic field at a general position outside the cable (r > R b ), showing your work. (Work in terms of symbols, not the numbers given below.) (b) Find the current density in the outer conductor, assuming the values: I 1 = 7.5 A, I 2 = 15.0 A, R a = 1.5 cm, and R b = 3.0 cm. (c) Viewed from the left and looking along the cable to the right, the magnetic field is, (choose one): (i) Clockwise in both the hollow between conductors and outside the cable. (ii) Along the axis, pointed away in the hollow, pointed toward you outside. (iii) Radially away from the center in both regions. (iv) Radially inward, both regions. (v) Clockwise inside, counterclockwise outside. (vi) Counterclockwise outside, clockwise inside. 5

5 (10) Three charges sit on the corners of a triangle as shown, with a and Q constants. What is the magnitude of the force on the charge in the lower left? (a) kq 2 / a 2 (b) 2kQ 2 / a 2 (c) 3kQ 2 / a 2 (d) 2kQ 2 / a 2 (e) 3kQ 2 / a 2 (11) A single-turn circular loop of wire sits in a B field, pointing perpendicular to the page. The loop has resistance 4.0 Ω, and cross-sectional area 0.85 m 2. The field changes as, B = B o sinωt, where positive means into the page (x s shown), B o = T, and ω = 6.0 rad/s. (a) Find an expression for the current vs. time in the loop, neglecting its self-inductance. What is the peak value of current? (b) At the time t = 0, will the induced current be clockwise or counterclockwise? (c) The net force on this loop due to the induced current and applied field will (choose one): (i) oscillate perpendicular to the page, up and down. (ii) be zero due to cancellation of vectors. (iii) be clockwise and counterclockwise, alternating with the appied field. (iv) point to the right. (v) point to the left. (vi) point right and left, in an oscillating fashion. (12) A converging lens has a focal length of 10 cm. A coin is placed 15 cm behind the lens. (a) Where will the image be located relative to the lens? (i) 10 cm (v) 30 cm (ii) 15 cm (vi) 35 cm (iii) 20 cm (iv) 25 cm (b) Will the image be behind the lens (object side) or in front of the lens (observer side)? 6

E) all of the above E) 1.9 T

E) all of the above E) 1.9 T 1. The figure shows a uniform magnetic field that is normal to the plane of a conducting loop, which has a resistance R. Which one of the following changes will cause an induced current to flow through