[l] Two point charges of 10.0 fj-c and +3.00 fic are separated by a distance of 20.0 cm. What are the magnitude and direction of the electric field midway between these two charges? [A] 0.63 X 10 7 N/C directed towards the negative charge J210.63 X 10 T N/C directed towards the positive charge ([Cj}l.l7 X 10 7 N/C directed towards the negative charge [D] 1.17 x 10 7 N/C directed towards the positive charge [E] 3.51 X 10 7 N/C directed towards the negative charge [2] The electric potential at x - 2.00 m is +200 V, and at x = 8.00 m is -1000 V. What is the magnitude and direction of the electric field? [A] 100 V/m in the -x direction (J5})200 V/m in the +x direction [C] 300 V/m in the -x direction [D] 400 V/m in the +x direction [E] 500 V/m in the -x direction [3] The resistivity of a 1.0 m long wire is 1.72 X 10~ 8 fi-m, and its cross sectional area is 1.0 X 10~ 6 m 2. If the wire carries a current of 0.10 A, what is the voltage across the wire? 7 mv [B] 3.4 mv [C] 16 mv [D] 20 mv [E] 34 mv [4] An electron moving perpendicular to a magnetic field of 4.2 X 10~ 2 T moves in a circle of radius 0.20 cm. How fast is this electron rnpving? [A] 2.5 x 10-53 m/s [B] 2500 m/s (lcj)l.5 x 10 7 m/s [D] 1.5 x 10 9 m/s [E] 8.0 x 10 9 m/s [5] A solenoid with a certain number of turns N, and carrying a current of 2.000 A, has a length of 34.00 cm. If the magnitude of the magnetic field generated at the center of the solenoid is 20.00 mt, what is the value of TV? [A] 1055 [B] 1353 [C] 1591 (JDj)2706 [E] 4601 [6] A conducting rod with a length of 25 cm is placed in a U-shaped metal wire that has a resistance R of 4.0 fi, as shown in the figure. The wire and the rod are placed in the plane of the paper. A constant magnetic field of strength 0.40 T is applied perpendicular into the paper. An applied force moves the rod to the right with a constant speed of 6.0 m/s. What is the magnitude and direction of the induced current in the wire? [A] 17 ma counterclockwise [B] 75 ma clockwise [D] 0.15 A clockwise ([El/ 0.15 A counterclockwise F applied [C] 75 ma counterclockwise
[7] The average intensity of the sunlight in Miami, Florida, is 1060 W/m 2. What is the average value of the radiation pressure due to this sunlight in Miami? [A] 2.28 x!0~ 6 N/m 2 @3.53 x!0~ 6 N/m 2 [C] 9.78 xlo~ 6 N/m 2 [D] 1.05 xlo~ 5 N/m 2 [E] 1.63 xlo~ 5 N/m 2 [8] A nearsighted person has a far point that is 2.6 m from his eyes. What focal length lenses must he use in his contact lenses to allow him to focus on distant objects? [A] -2.1 m [B] 2.1 m (fc)-2.6 m [D] 2.6 m [E] none of the above [9] What is the minimal non-zero thickness of a soap bubble (n = 1.42) that results in a constructive interference in the reflected light if this film is illuminated (at normal incidence) by a beam of light of wavelength 451 nm? ([AJ579 nm [B] 106 nm [C] 159 nm [D] 212 nm [E] 318 nm [10] Two spaceships approach Earth from opposite directions; one at a speed of 0.81c, and the other at a speed of 0.94c, both relative to Earth. What is the speed of one spaceship relative to the other? [A] 0.41 c [B] 0.45c [C] 0.54c (15) 0.9935c [E] 1.75c [ll] An electron is moving with a speed of 445 m/s. What is its de Brqglie wavelength? [A] 410 nm [B] 817 nm [C] 1000 nm [D] 1290 nm (JEJ)1630 nm [12] In a hydrogen atom, the electron makes a transition from the n = 8 to the n 4 state. What is the wavelength of the emitted photon? [A] 3.12 x 10~ 7 m [B] 9.54 x 10~ 7 m [C] 1.13 x 10~ 6 m (JDJ)l.94 x 10~ 6 m [E] 3.25 x ID" 6 m [13] Which one of the following is the correct ground state electronic configuration of the carbon atom (Z = 6)? [B] Is 2 2s 2 2p 6 [C] Is 2 2s 2 2p 6 3s 2 [D] Is 2 2s 2 2p 6 3s 2 3p 2 [14] Estimate the K a (i.e. due to a transition from the L shell to the K shell) X-ray wavelength for a gold atom (Z = 79 ). [A] 2.47 x 10~ 13 m @)2.00 x lo" 11 m [C] 3.60 x lo" 11 m [D] 5.13 x lo" 10 m [E] 8.54 x 10~ 10 m [15] Carbon-14 has a half-life of 5730 years. A sample of wood has been recovered by an archaeologist. The sample is sent to a laboratory, where it is determined that the activity of the sample is 0.104 Bq/g. By comparing this activity with the activity of living organic matter, 0.230 Bq/g, the scientist determines how old the wood sample is, or more precisely, when the tree that the sample came from died. How old is the sample of wood? [A] 2630 years [B] 3870 years [C] 4590 years [D] 5730 years ([E]) 6560 years
[16] The circuit shown in the figure consists of a 10.0-V battery, a 30.0-mH inductor, four 30.0-ft resistors, and a switch. (a) Find the time constant r for this circuit. (b) What is the current supplied by this battery three time constants after closing the switch? (c) How much energy is then stored in the inductor? (d) Assuming that the inductor is an air-filled solenoid of cross-sectional area 0.0300 m 2 and 450 turns, find its length. d-'., JM) So-o A d - u D A=o, ^ =5) {-^ L 3 a ~ IT LI 2 " o.o
[17] The observer in the figure is positioned so that the far edge of the bottom of the empty glass is just visible. When the glass is filled to the top with water (n = 1.33), the center of the bottom of the glass is just visible to the observer. Find the height, H, of the glass, given that its width is W 6.0 cm. H*l s^<u Svh^ \A/ JV^HH 1 W/i ^^TfH I ^ (Wf+H l -w- H') - ^ I/+ l*i L X?,.l \ i ; /i,, =, = t = 3.
[18] Consider the fusion reaction ^H +\ H > He + 7, where the (neutral) atomic masses are: m(le) = 2.014102 u, m( He) = 4.002603 u. (a) Write down an algebraic expression for the energy produced in this reaction in terms of m(ih) and m( He). (b) Calculate the energy produced in this reaction in MeV units. (c) How many kilowatt-hours (kwh) are released when 1.00 kg of deuterium (jh) undergo this reaction? / -D.D2S-CO/ f s H - - i n w ^ - - N U - ~
FORMULAE SHEET I e = 1.60 x 10~ 19 (7, m e = 9.11 x 2 2 = 8.99 x W 9 Nm 2 /C lev = 1.60 x 10-19 J, 10 6 J, e 0 = = 8.85 x W~ i2 C 2 /Nm 2 - V=, WE = qo. V', W nc = -^L r - K A n - - T- «' (2 ' 4 Ae 0 E "" 2 2 ""2C7' *" 2 ' A< (7 [l-erp(-i/t)], / = - exp (-i/r), g = Qexp = \q\vb, =?r x (bng), -, ' (coil) ' = NABusinwt, (solenoid) 2?r AJ X =- JS = E 0 sin(a;x -w<), fc = -^, E = cb, c = _ = 3.00 x 10 8 m/.s, \f = c
FORMULAE SHEET II c ~> n A vac = -n sin #1 = n 2 sin #2, sin$ c =, tan0 B =, = -f, J h h (double slit, grating, bright) infl = (m (double slit, dark) T> = f (single slit, dark) (resolution) (thin film, %$ ) r L = v = mv R = = 6.626 x 10~ 34 J 5 = 4.135 x 10~ 15 ef 5 = 1240 6 nm, a = = 1.054 x 10~ 34 J C 27T pr = 2.898 x, = 5.88 x E = hf =- = ^, c A \'-\ = A c = = 2.426pm m e c A db = -, > -, 2-2 = 0.0529 nm, E n - --B 0^-, ~ 2a0 = 13.6 o nq7v1fl7-1 -' ^ = = 1-097x10 m, n = l,2,3,...; t = 0,1,...,n - 1; m t = 0, ±1,..., ±1; m s = ±- T^, A = Z + 7V, r = r 0 A 1/3, r 0 = 1.2 /m = Amc 2, 1 u = 1.6605 x 10~ 27 A; 5 = 931.5 MeF/c 2, 7V A = 6.022 x lo^ ~ = \N, N = N 0 exp(-xt), X = ~, f = iln^, 1 Ci = 3.70 x Ac J i A xt A