s Physics 1B(b) Final Exam Winter 2010 Version A Problem 1: A parallel plate capacitor (dimensions 1 cm x 1 m) is designed to store energy. Putting a dielectric into the capacitor makes a huge difference to the amount of energy I can store. If I have a dielectric with a dielectric constant of k = 100 and the plates are spaced only 1 micron (10-6 m), how much energy can I store with 100 Volts across the capacitor? (Cb,q<j >t.id-1'j-. C,%, I'\.;y I D-Z ri' >CIH\) IL -_ a) 4.43 x 10-' J r" 100 ------------- Ia _Co (b 8.85 x 10-2.J W'- 2 C -::. (c) 4.43 X 10-4 J c:j,1/i '>( [o-g> r (d) 4.43 J - 0 f 72- C- V z ::::/2- ( g.'67>«0 -(" f )((67- V Y Problem 2: I have a square copper loop that is moving in an applied magnetic field B with velocity v. \Thich direction is the current in the loop? (a) clockwise (b) counterclockwise 1
\lq(jf'- A Problem 3: This is a hollow metal sphere. The sphere is charged with a charge of 1.0 x 10-9 Coulombs. \Vhat is the electric field just inside the inner surface (assume I mean at 0.9 em.)? (a) 1.11 x 10 3 NIC (b) 8.99 x 10 4 N/C (c) 1.11 X 10') N / C @0 Q -0 -) E=O. Problem 4: I have a charge of 1.0 x 10-6 Coulombs inside a cube of one meter on each side. \Vhat is the electric field flux coming out of each of the faces of the cube? (a) 1.13 x 1 [) Nm 2 (b) 1.88 x 10 4 Nm 2 (c) 2.26 x 10 5 Nm 2 /C (d) None of these C I O-Ct> C - '3, ==1 ' { >( \ 0 5 V'J;f,. I 2
al: Problem 5: I have stored energy in a capacitor of 10-6 F that has 100 V across it. How much current do I need in a 1 Henry inductor to store the same ' of energy? EC>f ;:c Y;<- v"- :: J.j: (I ere, FYIOZ V Y ::: \ 10- )J E f-,rj -;../2. /-T 2- = T Z ) ):ri'2= )('<f -z - I == O. (0 A aa't\l3 U,t\t Problem 6: I have a metallic sphere of radius 2.0 em. I charge the sphere 'Nith 1.0 x 10-8 C. I release an electron 5.0 em. away from the center of the sphere. \Vhat is the velocity of the electron when it hits the sphere? (a) 9.48 x 10 14 ml8 (b) 2.18 x 10 7 117./8 (c) 3.97 X 10 7 m/s (<1) 3.08 x 10 7 117./8 ( 2 = I-2.MV 2u'o" = +l.()xlo 1f C- l--?o. e -:-)V-.fl {/s
Problem 7: \Vhat is the equivalent capacitance of the following circuit? The capacitors are all have the same capacitance "C"? (a) 3.67 C C c.. (b) 9.0 C cr ) (d)1.0c C. C L J X.3 C, c....lc I '2C T Problem 8: I have two light bulbs that are 100 \V and 75 W. TXet the most light out of the pair of them, I should (a) connect them in series (b) connect them in parallel (c) doesn't matter f ::: ffi'2 fi5f 111-L -t1-e-r-:l -{k ia J M 1k ;jlq I 4
VOf'-l]) =C1I2 =T3-,)2At::tzc.T3 Problem 9, The emf of the battery is (%) [-(za.'f.( rl')-(jix '3j2 ) &f1oij> (b) 10.7 V (c) 8.3 V (d) 12.0 V L - )l'i?>).([ Jl't.- +'Z V =-0 - (GJL >-0 <jv 4 Ī.:: 2 A Problem 10: \Vhat is the time constant for this circuit, and what is the final charge on each capacitor after a long time"? (a) T = 3.0 X 10-6 5, ql = 4.0 x 1-7 C.,..q-.. = 4.0 X 10-7 C (b) T = 3.0 X 10-6 S = 3.0 X 10-7 C, q2 = 1.0 X 10-7 C (c) T = 1.0 X 10-6 5, ql = 3.0 X 10-7 C, q2 = 1.0 x 10- C (d) T = 3.0 X 10-6 s, ql = 4.0 X 10-7 C, q2 = 4.0 X 10-7 C V :. loo V) R \ = -:SOCCI 12 I «z. = (oco ills 11'e. C \ :::3)( {t>-t:t F I C,::' \ X lo-q f. Cv Q. ( C I V 3x \Of C QtC'2V,:- \x (D 1C.5
Problem 11: \Ve will design a magnet (solenoid) to do Functional l\.lagnetic Resonance Imaging (FMRI). \Ve want 2.5 Tesla with a length of 2 meters. The wire \vill carry 100 A in the superconducting state and will have a core diameter of 1 meter. How many windings do I need over the length of the coil? JI B:';Uot )1oH1 jl -) N::' _ Cl/)T'XZ) )}.o fto {(OO f\ ) E?fI11- Problem 12: \Vhat is the energy stored in the magnet in the previous question when it is carrying is full current of 100 A? (a) 3.91 x 10 4.J (b) 7.81 x 0 4.J (' c) 3.91 x 10).J ( 1.9.5 X 10 4.J r,., =- (L-(7\X (6 i,-%'x3q/f(11)'j..(7tlje. J-rA. -) vj,'1 ( I
Problem 13: An alpha particle (a helium atom missing two electrons, -! H e++) is accelerated in a Van de GraafI accelerator up to an energy of 2 IVleV(2 x 10 6 ev). It is fired into a region with a magnetic field B = 10 T. The alpha particle has a mass of 2 protons and 2 neutrons. \Vhat is the radius of the cyclotron orbit, and which way will the particle rotate? (a) 8.38 x 10-4 (t'-v - r;" -- m, clockwise. (b) 1.4-1x 10-2 m, clockwise at' (c) 1.44 X 10-2 tn, counter-clockwise (d) 1.70 X 10-1 111, counter-clockwise fl B 000 000 000 - -=,) =- 2..0Ji ')((0 2. fl\ I vj SQ " 16,73 'x)(oc.ev)( 1.Co><W f/ V), llg (O-l C'lO ro lem 14: I pu se a current in lie" irection indicated in coil 1. 'Which direction will the current in coil 2 be induced? (a) clockwise (b) counter-clockwise (c) no current in coils 7
VO'A f\ Problem 15: The switch is closed, and the light bulb glows, The light bulb resistance is 20 Ohms and the battery is 50 V, \Vhat is the time for the current to increase 6:3.2 percent of its maximum value? \Vhat is the maximum value? (a) 0.05 sand 0.4 A (b) 20 sand -4 A &fo.d? sand2i]) (d) 0.5 sand 2.5 A -r. - &;,32 _. 5,rctJ<. -t:: ""t- c- c- -r-::: =- \%52- =- 0.07 S ' VoQio.r rj.- f0 a.t,v-ll-: V - L-!if' - :L - () :=) V = T R )T= 2. SA Problem 16: 1 have a bar magnet enclosed in a cubic box. I hold it in two different orientations in the center of the box as shown. The magnetic flux <1> B emerging from the entire box (a) Greater when it points along the x, Y, or z direction (b) Greater when it points along the body diagonal... {J. (c) No difference \o..;;{k.. J y./ -ft,-e- S -9 ( "'. 8