PY Matte & Inteactions Final Exam S2005 Name (pint) Please cicle you lectue section below: 003 (Ramakishnan 11:20 AM) 004 (Clake 1:30 PM) 005 (Chabay 2:35 PM) When you tun in the test, including the fomula page, you must show an NCSU photo ID to identify youself Do not use othe pape If you need moe space, wite on the blank page included at the end of the test, and indicate that you did this Read all poblems caefully befoe attempting to solve them You wok must be legible, and the oganization must be clea You must show all you wok, including coect vecto notation Coect answes without adequate explanation will be counted wong Incoect wok o explanations mixed in with coect wok will be counted wong Coss out anything you don t want us to ead! Make explanations complete but bief Do not wite a lot of pose Include diagams! 3 6 a b ( 8x10 )( 5x10 ) Show what goes into a calculation, not just the final numbe: = c d 5 4 ( 2x10 )( 4x10 ) Give standad SI units with you esults = 5x10 Unless specifically asked to deive a esult, you may stat fom the fomulas given on the fomula sheet, including the equations coesponding to the fundamental concepts If a fomula you need is not given, you must deive it If you cannot do some potion of a poblem, invent a symbol fo the quantity you can t calculate (explain that you e doing this), and use it to do the est of the poblem 4 Poblem 1 (15 pts) Poblem 2 (20 pts) Poblem 3 (25 pts) Poblem 4 (10 pts) Poblem 5 (15 pts) Poblem 6 (30 pts) Poblem 7 (20 pts) Poblem 8 (30 pts) Total (165 pts) Make sue that no pages ae missing fom you test, and each poblem listed above appeas on you test SIGN THE HONOR PLEDGE: I have neithe given no eceived unauthoized aid on this test Sign you name on the line above
Poblem 1 (15pts) Two dipoles ae oiented as shown in the diagam Each dipole consists of two chages+6 nc and 6 nc, held apat by a od of length 15 mm (nc = nanocoulomb = 1e-9 coulomb) The location maked x is 8 cm fom the cente of each dipole dipole 2 dipole 1 8 cm The elative lengths of you aows fo pats a, b, and c below must be coect If any of the quantities asked fo is zeo you must state this explicitly (a: 2pts) On the diagam daw an aow epesenting the electic field vecto at the location maked x due to dipole1 and label it E1 (b: 2pts) On the diagam daw an aow epesenting the electic field vecto at the location maked x due to dipole 2 and label it E2 (c 2pts): On the diagam daw an aow epesenting the net electic field vecto at the location maked x and label it E net (d: 2pts) A small ball caying a chage of +7 nc unifomly distibuted ove its suface is placed at the location maked x Daw an aow epesenting the net electic foce on the ball and label it F (e: 7pts) What is the magnitude of the net electic foce on the ball? Show you wok
Poblem 2 (20 pts) A solid metal ball of adius 12 cm with a chage of -15 nc is located nea a hollow plastic ball of adius 23 cm that has a unifomly distibuted chage of 6 nc on its oute suface The distance between the centes of the balls is 9 cm plastic The elative lengths of you aows must be coect If any quantity is zeo you must state this explicitly (a: 9 pts) Sketch the appoximate chage distibutions on and/o in the plastic ball and the metal ball (b: 2pts) Daw an aow epesenting the electic field vecto at the cente of the metal ball due to the plastic ball alone Label it E pl metal (c: 2pts) Daw an aow epesenting the electic field vecto at the cente of the metal ball just due to the chages on the metal ball Label it (d: 2pts) Daw an aow epesenting the net electic field vecto at the cente of the metal ball Label it E m Enet (e: 5pts) Calculate the electic field at the cente of the metal ball due only to the chages in and/o on the metal ball Show you wok
Poblem 3 (25 pts) Two nichome wies of diffeent thickness ae pat of a lage steady state cicuit that is not shown on the diagam A conventional cuent of 6 ampees flows to the ight though the thicke wie The thicke wie has a diamete of 034 mm and a length of 20 cm The thinne wie has a diamete of 013 mm and a length of 30 cm (the diagam is not dawn to scale) Nichome has 9e28 electons/m 3 and the electon mobility is 7e-5 (m/s)/(n/c) connecting wies not shown A B connecting wies not shown 20 cm 30 cm (Diagam is not to scale: diamete of wies is geatly exaggeated) Calculate the potential diffeence V A V B, both magnitude and sign Show you wok
Poblem 4 (10 pts) You measue the potential diffeences between some of the locations shown at the ight, and find that V A V B = 11 volts V B V C = +7 volts V C V D = +5 volts (a: 5pts) What is V D V A? Show you wok A B C D (b: 5pts) What is V B V D? Show you wok
Poblem 5 (20 pts) A coil of wie of adius 3 cm, with 17 tuns of wie, is located on the x axis, a distance of 15 cm fom the oigin A cuent of 25 ampees uns though the coil in the diection shown on the diagam A compass is located at the oigin Magnetic Noth is in the z diection, as shown on the diagam y coil Noth I to batteies compass x z Calculate the compass deflection, both magnitude and diection Show you wok
Poblem 6 (30 pts) A lage cicula metal disk of adius 17 m has a chage of 3µC (µc = 1e-6 C) A long staight wie connected to a powe supply is located nea the chaged disk The disk and the wie ae placed nea a souce which poduces a beam of electons with a speed of 5e5 m/s in the +x diection Note that only the wie, the disk and a single electon (fo simplicity) ae shown in the diagam The wie is much longe and the disk much lage than ae shown in the diagam disk +3µC wie When the powe supply is not tuned on, so thee is no cuent unning though the long wie, the electons follow a cuved path (dotted lines in the diagam) and collide with the chaged disk Howeve, the electons tavel in a staight line though the egion when a cuent of 12 A flows though the wie (a: 2 pts) On the diagam daw an aow epesenting the electic foce on the electon due to the chaged disk Label it FE (b: 2pts) On the diagam daw an aow epesenting the magnetic foce vecto on the electon due to the cuent in the wie Label it FB (c: 6 pts) What is the diection of the electon cuent in the wie? Biefly explain you easoning (d: 20 pts) Calculate the distance between the electon beam and the wie Show you wok
Poblem 7 (20 pts) Compute inteface 1 N S initial position of magnet final position of magnet 2 You connect a 1300 tun coil of adius 35 cm to a compute inteface which measues the potential diffeence acoss the entie coil You have a ba magnet whose magnetic dipole moment is 13 Am 2 You hold the magnet, aligned as shown in the diagam, so its cente is 2 cm fom the cente of the coil Then you move it apidly away to a location whee its cente is 40 cm fom the cente of the coil You lab patne times you motion and epots that it took you 025 seconds to move the magnet (a: 6 pts) At each of the two locations indicated on the diagam, daw an aow indicating the diection of the electic field in the wie while you ae moving the magnet If eithe of these is zeo, state this explicitly Biefly explain you easoning (b: 14pts) Appoximately what is the absolute value of the emf that the compute inteface should display while you ae moving the magnet? Show all steps in you wok
Poblem 8 (30 pts) At time t=0, an electon at the oigin is acceleated (with an acceleation of 2e18 m/s 2 ) fo a vey shot time in the diection indicated in the diagam You ae at location A given by <0, -9, 0> m The x axis uns to the ight, the y axis uns towad the top of the page, and the z axis uns out of the page, towad you (a: 4 pts) On the diagam daw an aow showing the diection of popagation of the adiation that eaches you Label the aow v a (b: 4 pts) On the diagam daw an aow showing a Label it a 125 o (c: 4 pts) On the diagam daw an aow showing the diection of the electic field in the adiation eaching you Label the aow E (d: 4 pts) On the diagam daw an aow showing the diection of the magnetic field in the adiation eaching you Label the aow B (e: 4 pts) At what time do you fist detect electomagnetic adiation? Show you wok x 9 m A (f: 6pts) What is the magnitude of the adiative electic field that you obseve? Show you wok (g: 4pts) What is the magnitude of the adiative magnetic field that you detect? Show you wok
Fundamental Concepts Equations and pinciples you must know: (1) Electic field of a point chage (2) Relationship between electic field and electic foce (2) Magnetic field of a moving point chage (4) Relationship between magnetic field and magnetic foce on a point chage Consevation of Chage The Supeposition Pinciple Consevation of Enegy dp The Momentum Pinciple (Newton s 2d law): ----- = F o dt net ma = F net E ṋda E ṋ A q inside = --------------------- B nˆ da B nˆ A ε 0 = 0 B dl = µ 0 I inside path d + ε 0 ---- E nˆ da dt f d E dl = ---- B nˆ da dt q V = U V = V f V i = E dl E l i Specific esults Electic field of a unifomly chaged spheical shell: outside shell, like point chage; inside shell, 0 1 Q 1 E od = ----------- ------------------------------ a distance fom cente E if << L on axis 4πε od ----------- 2( Q L) 1 qz ------------------- E 0 2 + L 22 4πε 0 ing = ----------- ----------------------------- 4πε 0 ( z 2 + R 2 ) 3/ 2 E disk Q A z Q A z Q A = ----------- 1 ----------------------------- 2ε 0 ( z 2 + R 2 ) 12 / E disk ----------- 1 -- ----------- 2ε 0 R 2ε 0 if z << R E capacito Q A Q ----------- fo +Q and Q disks; E A s just outside capacito ε finge ----------- ------ 0 ε 0 2R 1 E dipole ----------- 2qs 1 -------- along dipole axis, fo x >> s; along axis, fo y >> s 4πε 0 x 3 E dipole ----------- ---- qs 4πε 0 y 3 i = nav I = q nav v = ue V = q ----------- 1 1 --- --- 4πε 0 f i due to point chage B µ 0 I l = ----- --------------- ˆ fo a shot segment of cuent-caying conducto 4π 2 F = I l B µ 0 LI µ 0 B wie ----- ----------------------------------- ----- 2I µ 0 NI = ---- fo << L B fo L >> R 4π 2 + ( L 2) 2 4π solenoid = ------------ L µ 0 2IπR 2 µ 0 B loop = ----- ----------------------------- on axis, z >> R cuent loop on axis 4π ( z 2 + R 2 ) 32 / ----- 2IπR2 -------------- 4π z 3 µ = IA = IπR 2 µ 0 B dipole ----- 2µ ----- 4π z 3 σ = qnu J I = -- = σe R A L = ------ I σa = V --------- R fo an ohmic esisto (R independent of V) powe = I V Q 1 = C V E adiative ----------- qa E = ----------- 4πε 0 c 2 vˆ = Ê Bˆ B = -- c Physical constants 1 9 ----------- 9 10 12 C = ------------- 4πε 0 C 2 ε 0 885 10 µ 0 7 = ------------ N m 2 ----- = 1 10 ------------- T m2 µ 4π C m/s 0 = 4π 10 7 ------------- T m2 C m/s 8 c = 3 10 m/s 19 e = 16 10 C 27 m poton m neuton = 17 10 kg 31 m electon = 9 10 kg 23 6 10 molecules/mole Atomic adius 10-10 m Poton adius 10-15 m g = 98 N/kg 6 Electic field necessay to ionize ai, about 3 10 N/C 5 B Eath 2 10 T (hoizontal component)