Physcs 114 1 Exam 3 The numbe of ponts fo each secton s noted n backets, []. Choose a total of 35 ponts that wll be gaded that s you may dop (not answe) a total of 5 ponts. Clealy mak on the cove of you blue book, whch ones ae to be gaded and not gaded. You must choose the twenty ponts woth that ae not to be gaded. 1. Souces of Magnetc Felds. a. [.5 ponts] Consde a we that s bent nto a ght angle at pont P that caes a cuent I = 3A What s the magntude of the magnetc feld at the pont P? b. [.5 ponts] What s the magntude and decton of the feld at q, assumng q s 1 m fom P and 1 mm fom the vetcal we? P q I c. [5 ponts] The fgue below s a coss-sectonal vew of a coaxal cable. The cente conducto s suounded by a ubbe laye, whch s suounded by an oute conducto, whch s suounded by anothe ubbe laye. In a patcula applcaton, the cuent n the nne conducto s I 1 = 1. A out of the monto, and the cuent n the oute conducto s I = 3. A nto the monto. (1) Detemne the magntude and decton of the magnetc feld at ponts a () Detemne the magntude decton of the magnetc feld at pont b.. Faaday s Law a. [.5 ponts] Imagne thee s a unfom magnetc feld pontng nto the page. (1) If a conductng ba s moved n a magnetc feld as shown below wth a constant velocty v, s thee an electc feld set up n the ba? () If so, what s the decton of that feld? (3) Is a foce equed to keep the ba movng? Explan.
X X X X X X X X X X X X X X X X B nto v X X X X X X X pape X X X X X X X X X X X X X X X X X X X b. [.5 ponts] Imagne now that the same ba s movng n the same feld (unfom nto the page) but t s now movng along metallc als as shown below. Would a foce be equed to keep the ba movng now? Explan. v c. [5 ponts] Consde the aangement shown above fo pat b. Assume that R = 6., l= 1. m, and a unfom.5 T magnetc feld s dected nto the page. (1) At what speed should the ba be moved to poduce a cuent of.5 A n the essto? () Wll that cuent be clockwse o counte clockwse when vewed fom above. (3) What s the tme ate of change of the flux closed ccut n the above pctue? dφ though the dt 3. Inductance a. [.5 ponts] A bass ng s placed on top of a col of we.(1) If a swtch to a souce of dect cuent s closed and chages stat to flow n the col, the ng spngs upwad. Explan. () The ng s then placed atop the col once agan, and the swtch opened. The cuent n the col apdly des out. What happens to the ng now? Explan. b. [.5 ponts] When the swtch s closed, the cuent though the ccut shown below, exponentally appoaches a value I=E/R. It takes a tme t1 to each a cuent of I/. If we epeat ths expement wth an nducto havng twce the numbe of
tuns pe unt length, what happens to the tme t takes fo the cuent to each a value of I/. c. [5 ponts] Consde the ccut shown below, takng ε = 6 V, L = 8. mh, and R = 4. Ω. (1) What s the nductve tme constant of the ccut? () Calculate the cuent n the ccut 5 µs afte the swtch s closed. (3) What s the value of the fnal steady-state cuent? (4) How long does t take the cuent to each 8% of ts maxmum value? 4. Electomagnetc waves. a. [.5 ponts] (1) What s the phase dffeence between the electc and magnetc felds composng an electomagnetc wave? () Descbe the physcal sgnfcance of the Poyntng vecto, what s t and what nfomaton does t povde? (3) In space salng, should you sal be eflectve o absoptve to be most effectve? b. [.5 ponts] At a fxed pont, P, the electc and magnetc feld vectos n an electomagnetc wave oscllate at angula fequency w. At what angula fequency does the Poyntng vecto oscllate at that pont? c. [5 ponts] In SI unts, the electc feld n an electomagnetc wave s descbed by Ey = 1 sn(1. x 1 7 x -ωt). (1) Calculate the ampltude of the coespondng magnetc feld. () Fnd the wavelength, (3) Fnd the fequency f. (4) Also fnd an expesson fo the vecto magnetc feld. 5. Natue of Lght a. [.5 ponts] (1) As lght tavels fom one medum to anothe, does t always bend towad the nomal? () Does ts fequency change? (3) Does ts wavelength change? (4) Does ts velocty change? Explan. b. [.5 ponts] Consde a lght ay of wavelength 6.33 nm (ed) oblquely ncdent on a slab of glass as shown below (ay 1). (1) Whch ays ae due to eflecton and whch ones ae due to efacton? () How does the angle that ay 1 makes wth the hozontal (θ 1 ) compae to that whch ay 5 makes wth the hozontal (θ )? (3) How do these angles compae to the angle ay 6 makes wth the hozontal (θ 3 )? (4) How would these angles change (θ and θ 3 ) f blue lght wee used nstead of ed? (5) What else, f anythng would change n the pctue?
1 5 θ 1 θ 3 4 θ 3 6 c. [5 ponts] Consde lght ncdent on the end of a ppe as shown below. Assume that the ppe has an ndex of efacton of 1.36 and the outsde medum s a. (1) Fo the ncdent angle θ, what wll be the ntal angle of efacton n the ppe (n tems of θ)? () Detemne the maxmum angle θ fo whch the lght ays ncdent on the end of the ppe ae subect to total ntenal eflecton along the walls of the ppe. (Hnt You need only examne the fst tme the ay goes fom the ppe to a). 6. Geometc Optcs a. [.5 ponts] (1) Daw the mage fomed of an obect (consstng of an upght aow) when t s placed cm n font of a thn, convex lens of focal length 1 cm. Be sue to clealy show at least two ays fomng the mage. Don t woy about tyng to daw dstances exactly. () Now daw the mage fomed by ths lens when the obect s placed 5 cm fom the lens. b. [.5 ponts] A thn lens s used to fom a eal mage of a neaby obect. If the obect s moved close to the lens, a new eal mage s obseved. Does the new mage dffe fom the old one (1) n poston elatve to the lens? () n sze? (3) If t does dffe n one of both of these, how so? c. [5 ponts] A sphecal mo s to be used to fom, on a sceen located 5 m fom the obect, an mage 5 tmes the sze of the obect. (1) Descbe the type of mo equed. () Whee should the mo be placed elatve to the obect?
Possbly Useful Infomaton. 1 q1 q F = ε = 885. X 1-1 ( C / N m ) 4πε e = 1.6 X 1-19 C E = F q q E = εφ= ε EdA. = q enc 4πε x = x - x 1, t = t - t 1 v = x / t s = (total dstance) / t v = dx/dt a = v / t a = dv/dt = d x/dt v = v o + at g = 9.8 m/s x-x o = v o t + (½)at = x $ + y $ + zk $ v = v o + a(x-x o ) = - 1 x-x o = ½( v o + v)t = (x - x1) + (y - y1) + (z - z1) k x-x o = vt -1/at v= / t, v=d/dt a = dv / dt a= v/ t U = U f - U = -W U=-W V = V f - V = -W/q = U/q V = -W /q V V f = E f. ds V= E. ds f 1 q n 1 q V = V = V 4πε = = 1 4πε = 1 1 dq V = 4πε V E s = V E s x E V y E V x = ; y = ; z = z V E = 1 q1q U = W = s 4πε 1 Q = CV A C = ε d l ab C = πε C = 4πε ln( b / a) b a C = 4πε R C = C (paallel) 1 1 C = eq C (sees) Q U = = 1 CV C eq n
u = 1 ε E C = κ C I= dq/dt ρ = 1 σ L R = ρ A V = IR P = IV P = I R=V /R I = ε ( R + ) P emf = Iε R = R (sees) 1 1 R = eq R (paallel) q(t)= Q(1-e -t/rc ) I = (ε/r)e -t/rc q(t) = Qe t/rc I = (Q/RC)e -t/rc, I = (Q/RC) F= qv x B F = IL x B d F = Ids x B τ = µ x B = NI A µ µ db = Ids x 4π 3, µ = 4π x 1-7 T. m/a B = µ I/ π B = µ ni (solenod) F/l = (µ I 1 I )/πa B.ds = µ I enc I = ε B = (µ IN)/(π) (tood) d dφ E dt Φ B = BdA. L = NΦ / I ε= Eds. N dφ B dt ε = -L di/dt L = µ n A/l I = I e -t/τ I = (ε/r)(1-e -t/τ ), τ = L/R U B = (1/)LI µ B = B /( µ ) c = ω/k = E/B = 1/( µ ε ) 1/ = 3. x 1 8 m/s= λf, ω = πf E = E max cos(kx-ωt) S = 1 µ Ex B I = E max /(c µ ) = S av I = P s /4π P = S/c n = c/v p = I/c, p = I/c I = ½ I, I = I cos (θ) n 1 sn(θ 1 ) = n sn(θ ) θ c = sn -1 (n /n 1 ) 1/f = 1/p + 1/q = /R n 1 /p + n /q = (n - n 1 )/R 1/f = (n-1)(1/r 1-1/R ) M = - q/p, M = h /h n = λ /λ eq