GENERAL PHYSICS PH -A (MIROV) Exam 3 (03/31/15) STUDENT NAME: STUDENT i #: ------------------------------------------------------------------------------------------------------------------------------------------ WORK ONLY 5 QUESTIONS ALL QUESTIONS ARE WORTH 30 POINTS ------------------------------------------------------------------------------------------------------------------------------------------ NOTE: Clearly write ut slutins an answers (circle the answers) by sectin fr each part (a., b., c., etc.) Imprtant Frmulas: Ch.8. Magnetic fiels 1. Magnetic frce exerte n a pint charge by a magnetic fiel: F q v i. The number ensity n f charge carriers (Hall Effect): n Vle mv 3. Circular rbit in magnetic fiel: r q 4. Magnetic frce n a straight current carrying wire f length L: F il 5. The frce acting n a current element in a magnetic fiel: F il 6. Magnetic iple mment f current lp: = [current] x [area] 7. Trque n a current carrying cil: 8. Orientatin energy f a magnetic iple: U ( ) 9. The wrk ne n the iple by the agent is: W a U U f U i 10. Permeability cnstant: = 1.6x10-6 Ns /C = 1.6x10-6 H/m; 11. Permittivity cnstant: = 8.85x10-1 C /(Nm ) = 8.85x10-1 F/m; Ch. 9 Magnetic fiels ue t currents ˆ i s r 1. The i-savart Law: 4 r I. Magnetic fiel f a lng straight wire current: 0 {Unit 1 tesla = 1T = 1 N/(Cm/s)} r 3. Magnetic fiel f a circular arc: i 4 R L i aib 4. Frces between parallel currents: F ba ibl a sin 90 5. Ampere s Law: s i e n c 6. Magnetic fiel f an ieal sleni: in 1 7. Magnetic fiel f a tri: in r
1. Fiel f a magnetic iple: ( z ) 3 z Ch. 30. Inuctin an Inuctance 1. Magnetic flux: A {Unit 1weber = 1Wb = 1 T m }. Faraay s Law f Inuctin: t 3. Lenz Law: Inuce emf ppses change that pruce it 4. Emf an the Inuce Electric Fiel: E s t N 5. Inuctance: L {SI unit henry(h), where 1 H=1Tm /A) i L 6. The inuctance per unit length f sleni: n A l i 7. Self-inuctin: L L t i 1 1 i 8. Mutual inuctin: M ; M ; 1 M i1 i t t t L i (1 e ) (rise f current) 9. Series RL Circuits: R t L i i e (ecay f current) 1 U L i (m agnetic energy) 10. Magnetic Energy: u (m agnetic energy ensity) Ch. 31. Electrmagnetic Oscillatins an Alternating Current q L i 1. LC Energy transfer: U E, U, U U E U c n s t C. Emf f an electrmagnetic generatr: = - /t=na sin( t) 1 3. LC Charge an Current Oscillatins: q Q cs( t ); ; i Q sin( t ) LC Rt L 4. Dampe Oscillatins: q Q e cs( ' t ), w here ' R L 5. Alternating Currents; Frce Oscillatins: A se rie s R L C c irc u it m a y b e se t in t f rc e sc illa ti n a t a riv in g a n g u la r frequency by an external alternating em f = sin t; i I sin( t ) m
1. Resnance: I m when. Then X C X L, R 0. Capacitive reactance: V C =IX C ; X C 1 C ; the current leas vltage by / raians (=- / ra) 3. Inuctive reactance: V L =IX L ; X L L ; the current lags behin the vltage by / raians(=/ ra) 4. Series RLC Circuits Relatin between emf an current: m =IZ Impeance: Z R X X L C Phase angle between current an vltage: tan X L X C R Average Pwer issipate: Pavg I rmsr rmsi rms cs, I rms I / ; V rms V / ; rms / Pwer factr f the circuit: cs 5. Transfrmers: V I s s p p s p p s (transfrm atin f vltage) (transfrm atin f currents) The equivalent resistance f the secnary circuit, as seen by the generatr R eq V I N N N N N N p s R, where R is the resistive la f the secnary circuit Ch. 3. Maxwell s Equatins. Magnetism f matter 1. Gauss Law fr Magnetic Fiel: A 0. Maxwell s Extensin f Ampere s Law: S 0 0 0ienc t E 3. Displacement current: i 0 t
1. The rectangular lp shwn in Figure is pivte abut y axis an carries a current f 15.0 A in the irectin inicate. a) Fin magnitue an irectin f the lp magnetic iple mment. b) If the lp is in unifrm magnetic fiel with magnitue 0.48 T in the +x irectin, fin the magnitue an irectin f the trque require t hl the lp in the psitin shwn. c) What is the irectin in which the lp tens t rtate?
. A circular lp has raius R an carries current I in a clckwise irectin. The center f the lp is a istance D abve a lng straight wire. What are the magnitue an irectin f the current I 1 in the wire if the magnetic fiel at the center f the lp is zer?
3. A lng, straight, sli cyliner, riente with its axis in the Z-irectin carries a current whse current ensity is J. The current ensity, althugh symmetric abut the cyliner axis, is nt cnstant but varies accring t relatinship I r J 1 k fr r a a a 0 fr r a Where a is the raius f the cyliner, r is the raial istance frm the the cyliner axis, an I is a cnstant having units f amperes. a) Shw that I is the ttal current passing thrugh the entire crss-sectin f the wire. b) Obtain the expressin f the current I cntaine in a circular crss-sectin f raius r a an centere at the cyliner axis. c) Using Ampere s law, erive an expressin fr the magnitue f the magnetic fiel insie in the regin r a.
4. The rawing shws a plt f the utput emf f a generatr as a functin f time t. The cil f this evice has a crss-sectinal area per turn f 0.00 m an cntains 150 turns. Fin: a) The frequency f f the generatr in hertz; b) The angular spee in ra/s; an c) The magnitue f the magnetic fiel.
5. A frien returns t the Unite States frm Eurpe with a 960-W cffeemaker, esigne t perate frm 40-V line. A) Determine the ratin N s /N p f the transfrmer necessary t perate the cffeemaker in the Unite States. ) What current will the cffeemaker raw frm the 10-V line? C) What is the resistance f the cffeemaker? (The vltages are rms values.)
7. An scillating LC circuit has current amplitue f 7.50 ma, ptential amplitue f 50 mv, an a capacitance f 0 nf. What are: a) The peri f scillatin; b) The maximum energy stre in the capacitr; c) The maximum energy stre in the inuctr; ) The maximum rate at which the current changes; an e) The maximum rate at which the inuctr gains energy. (a) Frm V = IX C we fin = I/CV. The peri is then T = / = CV/I = 46.1 s. (b) The maximum energy stre in the capacitr is U E 1 1 (.0 10 7 F)(0.50 V) 6.88 10 9 CV J. (c) The maximum energy stre in the inuctr is als U LI / 6.88 nj. () V = L(i/t) max. We can substitute L = CV /I an slve fr (i/t) max. Our result is 3 i V V I (7.50 10 A) 7 t L CV / I CV (.010 F)(0.50 V) max 3 1.0 10 A/s. (e) The erivative f U = 1 Li leas t U t 1 LI sin t cst LI sin t. Therefre, U t max 1 1 1 (7.50 10 3 LI IV A )(0.50 V ) 0.938 m W.