AP Physics C: Electricity and Magnetism 2001 Scoring Guidelines

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AP Physics C: Electicity and Magnetism 1 Scoing Guidelines The mateials included in these files ae intended fo non-commecial use by AP teaches fo couse and exam pepaation; pemission fo any othe use

1 AP Physics C: Electicity and Magnetism 1 Scoing Guidelines The mateials included in these files ae intended fo non-commecial use by AP teaches fo couse and exam pepaation; pemission fo any othe use must be sought fom the Advanced Placement Pogam. Teaches may epoduce them, in whole o in pat, in limited quantities, fo face-to-face teaching puposes but may not mass distibute the mateials, electonically o othewise. These mateials and any copies made of them may not be esold, and the copyight notices must be etained as they appea hee. This pemission does not apply to any thid-paty copyights contained heein. These mateials wee poduced by Educational Testing Sevice (ETS), which develops and administes the examinations of the Advanced Placement Pogam fo the College Boad. The College Boad and Educational Testing Sevice (ETS) ae dedicated to the pinciple of equal oppotunity, and thei pogams, sevices, and employment policies ae guided by that pinciple. The College Boad is a national nonpofit membeship association dedicated to pepaing, inspiing, and connecting students to college and oppotunity. Founded in 19, the association is composed of moe than 3,9 schools, colleges, univesities, and othe educational oganizations. Each yea, the College Boad seves ove thee million students and thei paents,, high schools, and 3,5 colleges, though majo pogams and sevices in college admission, guidance, assessment, financial aid, enollment, and teaching and leaning. Among its best-known pogams ae the SAT, the PSAT/NMSQT, the Advanced Placement Pogam (AP ), and Pacesette. The College Boad is committed to the pinciples of equity and excellence, and that commitment is embodied in all of its pogams, sevices, activities, and concens. Copyight 1 by College Entance Examination Boad. All ights eseved. College Boad, Advanced Placement Pogam, AP, and the acon logo ae egisteed tademaks of the College Entance Examination Boad.

2 1 SCORING GUIDELINES Geneal Notes about 1 AP Physics Solutions 1. The solutions contain the most common method(s) of solving the fee-esponse questions, and the allocation of points fo these solutions. Othe methods of solution also eceive appopiate cedit fo coect wok.. Geneally, double penalty fo eos is avoided. Fo example, if an incoect answe to pat (a) is coectly substituted into an othewise coect solution to pat (b), full cedit will usually be awaded. 3. An exception to this may be cases when the numeical answe to a late pat should be easily ecognized as wong, e.g., a speed faste than the speed of light in vacuum. 4. Implicit statements of concepts nomally eceive cedit. Fo example, if use of the equation expessing a paticula concept is woth one point, and a solution contains the application of the equation to the poblem but does not sepaately list the basic equation, the point is still awaded. Copyight 1 by College Entance Examination Boad. All ights eseved.

3 1 SCORING GUIDELINES Question 1 15 points total 1. (a) 4 points Distibution Fo a coect fomula fo detemining the electic field E = kq ˆ o = kq ˆ E Summing the contibutions to the field fom the fou chages, letting fields diected upwad be positive and fields diected downwad be negative (full cedit also given fo using opposite convention as long as answes wee consistent): ( 9 1 )( 3) ( 9 1 )( 3) ( 9 1 )( 3) ( 9 1 )( 3) E = Fo coect substitutions shown in the above equation E = 3, N C + 67,5 N C + 67,5 N C 3, N C E = 75, N C, diected upwad Fo coect magnitude ( E = o k( 8 1 ) also accepted) 4π Fo coect diection, eithe stated o shown by an upwad diected aow Notes: If wong signs wee used in the substitution, the point fo coect magnitude was not awaded. If calculation was done using only the two eal chages, a maximum of 3 points was awaded as follows: fo the fomula, fo the calculation, fo diection. 1. (b) i. Fo coectly indicating diection, such as by an upwad diected aow at point P, 1. (b) ii. points Fo coectly checking the space in font of Less Fo coect justification, such as P is fathe fom all the chages than P 1, so the net field is less. If student chose to wok out the actual magnitude of the field at P (which is about 45, N/C), the justification point was awaded fo any calculated numeical value less than 75, N/C. Note: No points wee awaded fo (b) ii. if the wong space was checked. Copyight 1 by College Entance Examination Boad. All ights eseved. 3

4 1 SCORING GUIDELINES Question 1 (cont.) 1. (c) i. points Distibution The potential at P 1 is, which can be detemined without calculation fom symmety consideations. Fo stating V = o fo just points Altenate Solution Fo a coect fomula fo detemining the potential V = kq V = k + = 3 3 Fo the coect answe Altenate points 1. (c) ii. points The potential at P is, which can also be detemined without calculation fom symmety consideations. Fo stating V = o fo just points Altenate Solution Fo a coect fomula fo detemining the potential V = kq V = k = Fo the coect answe Altenate points 1. (d) points Fo a coect fomula fo detemining the potential V = kq Fo coect substitution of values (no cedit lost fo failing to convet kilometes to metes) VP = k + ( 3 1) 1 3 ( 1) 1 3 ( + 1) 1 3 ( 3+ 1) = V 1 V V P Copyight 1 by College Entance Examination Boad. All ights eseved. 4

5 1 SCORING GUIDELINES Question 1 (cont.) 1. (e) points Distibution Fo a coect fomula fo the potential enegy (must include a summation sign) qq U = k i j o U = qv i, j ij Fo coect substitution without egad to sign eo (no cedit lost fo failing to convet kilometes to metes) 1 U = J ( ) ( ) ( ) ( ) U = ( 9 1 ) J Copyight 1 by College Entance Examination Boad. All ights eseved. 5

6 1 SCORING GUIDELINES Question 15 points total. (a) 4 points Distibution Thee wee thee methods geneally used to solve this poblem. Method 1. Fo a coect method based on detemining the time constant using values fom the gaph τ= RC 6 min = 36 s Fo coect substitution of values with pope units τ 36 s R = = C F Fo answe consistent with values used 8 R = Ω points Method. V = V e trc Fo using the above equation with given value of C and values fo V, V, and t fom the gaph with t coelating with V Example: V = 1 V, and V = V at t = 1 min Fo coect substitution of values 6 ( 6 s) R( 8 1 F) = 1e ln 1 = 6 R Fo answe consistent with values used 8 R = Ω points Method 3. Find a coect elationship that depends on the slope of the gaph: V V Example: R = = i dq dt But dq = CdV V So R = C ( dv dt ) Fo estimating dv dt by computing V t fo a paticula value of V points Fo substituting values in equation above Fo answe consistent with values used Note: The value used fo V must be that at the point whee the slope is taken and clealy indicated. Copyight 1 by College Entance Examination Boad. All ights eseved. 6

7 1 SCORING GUIDELINES Question (cont.). (b) 3 points Distibution Fo a coect equation fo the capacitance κ A C = d Fo coect algebaic solution fo aea A and substitution of vaiables 6 4 Cd ( 8. 1 F)( 1. 1 m) A = = -1 κ C N m Fo the coect answe A =16 m. (c) 3 points Fo a coect equation fo the esistance ρ R = L A Fo coect algebaic solution fo esistivity H and substitution of vaiables RA ( Ω)( 16 m ) ρ = = -4 L 1. 1 m Fo answe consistent with values used 13 ρ = 7. 1 Ω m Copyight 1 by College Entance Examination Boad. All ights eseved. 7

8 1 SCORING GUIDELINES Question (cont.). (d) 4 points Distibution Thee wee fou geneal methods fo solving this poblem. Solutions wee scoed as follows: Fo using a coect method Fo substituting appopiate values Fo answe consistent with values obtained in ealie pats points Method 1: Q= C V, and substitute values obtained fom gaph 6 Example: ( i = F)( 1 V) Q f = 8. 1 F V 5 So Q = C o 64 C Q and Method : 6 t 6 6 V t 1 V t trc t36 Q = I dt = e dt = Ω e dt R (. 1 )( 36) 8 t 36 6 s Q= e C o 65 C Q = Method 3: Q= CV e trc s ( Ω )( 8. 1 F) Q= ( 8. 1 F)( 1 V ) 1 e 5 Q = C o 65 C Method 4: Detemine the aea unde the cuve of I vs.t, which is the V vs.t gaph shown with I = V R. Each block has aea equal to Vt R = C. Estimating 47 blocks unde the cuve gives 5 Q = C o 63 C Unit point: Fo coect units given on answes fo thee of the fou pats Copyight 1 by College Entance Examination Boad. All ights eseved. 8

9 1 SCORING GUIDELINES Question 3 15 points total 3. (a) points Distibution Using Ohm s law: V = IR Fo coect equation fo I ε I = R Fo coectly indicating the cuent diection on the diagam o in the answe space, such as by stating that it is clockwise, o to the left, o by showing an aow pointing left 3. (b) 4 points Fo indicating on the diagam o in the answe space a diection opposite to the answe in pat (a). If pat (a) does not contain a diection, then fo an indication that the diection is to the ight o by showing an aow pointing ight. Fo a complete justification Full cedit awaded fo an answe that indicated the ight-hand ule to obtain the magnetic field diected out of the page at the od, and then used the coss poduct to obtain that the foce on the od is up points patial cedit awaded fo an answe that just stated the ule that antipaallel cuents epel o that just stated I l x B and the ight-hand ule patial cedit awaded fo an answe that just stated the ight-hand ule o I l x B o some fagment with some coect element 3 points 3. (c) 4 points Fo indicating that the gavitational foce will be equal to I l x B F = I l x B = mg Fo giving the coect equation fo the magnetic field µ i B = π Fo coectly substituting in the fist equation above the values fo B and fo I fom pat (a) µ I cε = mg π R Fo the coect answe π mgr I c = µ ε Copyight 1 by College Entance Examination Boad. All ights eseved. 9

10 1 SCORING GUIDELINES Question 3 (cont.) 3. (d) 5 points Distibution Fo the coect expession fo φ µ φ = Ic B da, whee B =, and x is the vetical distance fom the cable π x Letting da = dx and substituting the values fo B above and fo I c fom pat (c): + dµ π mgr dx φ = πµ ε x Fo coect limits of integation Fo coect substitution of the values consistent with pevious answes Fo coect integation mgr + d φ = ln x ε Fo the coect answe mgr + d φ = ln ε Copyight 1 by College Entance Examination Boad. All ights eseved. 1

AP Physics C: Electricity and Magnetism 2003 Scoring Guidelines

AP Physics C: Electricity and Magnetism 2003 Scoring Guidelines AP Physics C: Electicity and Magnetism 3 Scoing Guidelines The mateials included in these files ae intended fo use by AP teaches fo couse and exam pepaation; pemission fo any othe use must be sought fom