Physics C: Electricity and Magnetism

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1 Physics C: Electicity an Magnetism

2 TABLE OF INFORMATION FOR CONSTANTS AND CONVERSION FACTORS - unifie atomic mass unit, u = kg = 93 MeV/ c Poton mass, m p = kg Neuton mass, m n = kg Electon mass, m e = 9. 3 kg Magnitue of the electon chage, e = 6. 9 C Avogao s numbe, N = 3 6. mol Univesal gas constant, R = 83. J/ ( mol ¼ K ) Boltzmann s constant, k B = J/K Spee of light, c = 3. 8 ms / Planck s constant, h 34 = 663. Js = ev s 5 hc = 99. J m 3 = 4. ev nm Vacuum pemittivity, = 885. C / N m 9 Coulomb s law constant, k = / 4π = 9. Nm / C Vacuum pemeability, 7 µ = 4π ( Tm) / A Magnetic constant, k = µ / 4π = 7 ( T m) / A Univesal gavitational constant, G = m 3 / kg ¼s Acceleation ue to gavity at the Eath s suface, g = 98. m/s atmosphee pessue, atm 5 =. N /m 5 =. Pa electon volt, ev = 6. 9 J UNITS Name Symbol mete kilogam secon ampee kelvin mole hetz newton pascal joule watt coulomb volt ohm heny faa tesla egee Celsius electonvolt m kg s A K mol Hz N Pa J W C V Ω H F T o C ev PREFIXES Facto Pefi Symbol 9 giga G 6 mega M 3 kilo k centi c 3 milli m 6 mico µ 9 nano n pico p VALUES OF TRIGONOMETRIC FUNCTIONS FOR COMMON ANGLES θ sin θ cos θ tan θ o 3 o / 3 / 33 / 37 o 3/5 4/5 3/4 45 o / / 53 o 4/5 3/5 4/3 6 o 3 / / 3 9 o The following conventions ae use in this eamination. I. Unless othewise state, the fame of efeence of any poblem is assume to be inetial. II. The iection of any electic cuent is the iection of flow of positive chage (conventional cuent). III. Fo any isolate electic chage, the electic potential is efine as zeo at an infinite istance fom the chage.

3 ADVANCED PLACEMENT PHYSICS C EQUATIONS FOR MECHANICS ELECTRICITY AND MAGNETISM u = u + at a = acceleation qq A = aea F = foce F = 4p B = magnetic fiel = + ut + at f = fequency h = height u = u + a - 5 E = F C = capacitance = istance I = otational inetia q E = electic fiel Ê F = Fnet = ma J = impulse Q e = emf p K = kinetic enegy E A= F = foce F = t k = sping constant I = cuent l = length V L = inuctance J = I F t = Dp E = L = angula momentum l = length p = mv m = mass q n = numbe of loops of wie pe i Ffic ˆ mn N = nomal foce V = unit length P = powe 4p i i P = powe W = I F œ p = momentum qq Q = chage K = m = aius o istance UE = qv = u 4p q = point chage = position vecto W P = T = peio C Q R = esistance = = istance t t = time V t = time P = F v U = potential enegy k A U = potential o stoe enegy DUg = mgh u = velocity o spee C = V = electic potential W = wok one on a system υ = velocity o spee u ac = = w = position Cp = Ci = esistivity i m = coefficient of fiction f t = F m = magnetic flu q = angle = k = ielectic constant Ê t = tnet = Ia t = toque Cs i Ci w I = I m = Ê m = angula spee Q a = angula acceleation I = cm = Ê m Ê m t u = w Uc = Q V = CV L = p = Iw l K = Iw R = A w = w + at V = IR q = q + wt + at R = R s i i Fs =-k = Us = k R i R p i p P= IV T = = w f FM = qv B m Ts = p B ø = m I k Tp = l F= I Iø B p g Bs = mni Gmm FG =- $ f m = I B A fm Gmm e = UG =- t e =L I t UL = LI 3

4 ADVANCED PLACEMENT PHYSICS C EQUATIONS FOR GEOMETRY AND TRIGONOMETRY Rectangle A = bh Tiangle A = bh Cicle A = p C = p Paallelepipe V = lwh Cyline V = p l S = pl + p Sphee V = 4 3 p 3 S = 4p Right Tiangle a + b = c sin q = a c b cos q = c tan q = a b CALCULUS A = aea C = cicumfeence V = volume S = suface aea b = base h = height l = length w = with = aius q c b 9 a f = n e n 7 7 f u u = n = e n - ( ) = ( sin ) = cos ( cos ) =-sin n n + I = n + e= e I = n I cos = sin I sin =-cos, n ž- 4

5 AP PHYSICS C: ELECTRICITY AND MAGNETISM FREE-RESPONSE QUESTIONS PHYSICS C Section II, ELECTRICITY AND MAGNETISM Time 45 minutes 3 Questions Diections: Answe all thee questions. The suggeste time is about 5 minutes fo answeing each of the questions, which ae woth 5 points each. The pats within a question may not have equal weight. Show all you wok in the pink booklet in the spaces povie afte each pat, NOT in this geen inset. E&M. - A o of unifom linea chage ensity l = C m is bent into an ac of aius R =. m. The ac is place with its cente at the oigin of the aes shown above. (a) Detemine the total chage on the o. (b) Detemine the magnitue an iection of the electic fiel at the cente O of the ac. (c) Detemine the electic potential at point O. A poton is now place at point O an hel in place. Ignoe the effects of gavity in the est of this poblem. () Detemine the magnitue an iection of the foce that must be applie in oe to keep the poton at est. (e) The poton is now elease. Descibe in wos its motion fo a long time afte its elease. Copyight by College Entance Eamination Boa. All ights eseve. Avance Placement Pogam an AP ae egistee taemaks of the College Entance Eamination Boa. 5 GO ON TO THE NEXT PAGE.

6 AP PHYSICS C: ELECTRICITY AND MAGNETISM FREE-RESPONSE QUESTIONS E&M. You engineeing fim has built the RC cicuit shown above. The cuent is measue fo the time t afte the - switch is close at t = an the best-fit cuve is epesente by the equation It 5= 5e t /., whee I is in milliampees an t is in secons. (a) Detemine the value of the chaging voltage V peicte by the equation. (b) Detemine the value of the capacitance C peicte by the equation. (c) The chaging voltage is measue in the laboatoy an foun to be geate than peicte in pat (a). i. Give one possible eplanation fo this fining. ii. Eplain the implications that you answe to pat i has fo the peicte value of the capacitance. () You laboatoy supeviso tells you that the chaging time must be ecease. You may a esistos o capacitos to the oiginal components an econnect the RC cicuit. In pats i an ii below, show how to econnect the cicuit, using eithe an aitional esisto o a capacito to ecease the chaging time. i. Inicate how a esisto may be ae to ecease the chaging time. A the necessay esisto an connections to the following iagam. ii. Instea of a esisto, use a capacito. Inicate how the capacito may be ae to ecease the chaging time. A the necessay capacito an connections to the following iagam. Copyight by College Entance Eamination Boa. All ights eseve. Avance Placement Pogam an AP ae egistee taemaks of the College Entance Eamination Boa. 6 GO ON TO THE NEXT PAGE.

7 AP PHYSICS C: ELECTRICITY AND MAGNETISM FREE-RESPONSE QUESTIONS E&M 3. A cicula wie loop with aius. m an esistance 5 W is suspene hoizontally in a magnetic fiel of magnitue B iecte upwa at an angle of 6 with the vetical, as shown above. The magnitue of the fiel in teslas is given as a function of time t in secons by the equation B = 4(.t). (a) Detemine the magnetic flu f m though the loop as a function of time. (b) Gaph the magnetic flu f m as a function of time on the aes below. Copyight by College Entance Eamination Boa. All ights eseve. Avance Placement Pogam an AP ae egistee taemaks of the College Entance Eamination Boa. 7 GO ON TO THE NEXT PAGE.

8 AP PHYSICS C: ELECTRICITY AND MAGNETISM FREE-RESPONSE QUESTIONS (c) Detemine the magnitue of the inuce emf in the loop. () i. Detemine the magnitue of the inuce cuent in the loop. ii. Show the iection of the inuce cuent on the following iagam. (e) Detemine the enegy issipate in the loop fom t = to t = 4 s. END OF SECTION II, ELECTRICITY AND MAGNETISM 8

AP Physics C: Electricity and Magnetism 2004 Free-Response Questions

AP Physics C: Electricity and Magnetism 2004 Free-Response Questions AP Physics C: Electricity an Magnetism 004 Free-Response Questions The materials inclue in these files are intene for noncommercial use by AP teachers for course an exam preparation; permission for any