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AP PHYSICS C: ELECTICITY AND MAGNETISM 3 SCOING GUIDELINES Question 1 15 points total Distibution Answes shown hee ae expessed in tems of Coulomb s law constant k, but equivalent answes in tems of 1Fε wee acceptable. (a) The sphee of chage can be teated as a point chage located at the sphee s cente. i. ( points) kq E = Fo indicating that the total chage is Q Fo a coect answe kq E = ii. () Fo a coect answe kq V = Cedit was also awaded fo integating E to obtain V (b) Fo indicating that the poton will move away fom the chaged sphee Fo indicating that the velocity of the poton will incease o each a finite value Fo indicating that the acceleation of the poton will decease (c) Fo a coect statement of consevation of enegy K = U U Fo the substitution of an electical potential enegy with the coect fom keq keq K = Fo a coect answe 1 1 K keq = Copyight 3 by College Entance Examination Boad. All ights eseved. Available at apcental.collegeboad.com.
AP PHYSICS C: ELECTICITY AND MAGNETISM 3 SCOING GUIDELINES (c) (continued) Question 1 (cont d.) Distibution Altenate solution Fo showing coect use of the wok-enegy theoem K = W = F d Fo setting up the coect integation kqe K = d 1 1 1 1 1 K = kqe = kqe = kqe Fo a coect answe 1 1 K keq = Altenate points (d) H can be detemined by integating the volume distibution and setting it equal to the total chage Q Fo indicating that an integation is necessay ( ) Q= H dv Fo showing a coect volume element dv = π d H and dv Fo substitution of ( ) Q= H 1 d F 3 3 3 3 3 Q= FH d = FH = = 3 FH 3 FH 1 3Q H = 3 F Copyight 3 by College Entance Examination Boad. All ights eseved. Available at apcental.collegeboad.com. 3
AP PHYSICS C: ELECTICITY AND MAGNETISM 3 SCOING GUIDELINES Question 1 (cont d.) Distibution (e) Fo witing Gauss s law with a chage element dq O showing the elationship between E and dq 1 k E da= dq ε O de = dq 1 k E F = H( ) dv O E = ( ) dq A H Fo coect substitution of H, dv, and coect limits 3Q H( ) dv = 1 d 3 F F 3 3 1Q 1Q Q 3 3 H ( ) dv = d 3 3 3 = = 3 1 Q 3 3 E = 3 πε Fo a coect answe kq 3 E = 3 O E k Q 3 3 = 3 Copyight 3 by College Entance Examination Boad. All ights eseved. Available at apcental.collegeboad.com.
AP PHYSICS C: ELECTICITY AND MAGNETISM 3 SCOING GUIDELINES Question 15 points total Distibution (a) points Fo including the esisto, capacito, battey and switch elements with common symbols and clea labels in the diagam One point was deducted fo using one uncommon symbol o mislabeling one element No cedit was given fo a cicuit missing any elements o with two o moe uncommon symbols o mislabeled elements Fo coectly showing the esisto, capacito, and battey connected in seies Fo placing the ammete in seies with the esisto points (b) Fo any statement of Ohm s law = V I One point each fo substituting the values of the initial conditions consistent with the gaph into the above equation = 1 V.1 A ( ) ( ) = 1 Ω points Altenate solution Fo using the given equation fo the cuent ε t () = e i t Fo substituting consistent cuent and time values fom the gaph into the above equation Fo a value of esistance consistent with the substituted values Altenate points Copyight 3 by College Entance Examination Boad. All ights eseved. Available at apcental.collegeboad.com. 5
AP PHYSICS C: ELECTICITY AND MAGNETISM 3 SCOING GUIDELINES (c) points Question (cont d.) Distibution Fo the equation fo the time constant τ = C Fo substituting the value of the time constant fom the given equation fo cuent, i.e. s Fo substituting the esistance fom pat (b) C = s 1 Ω ( ) ( ) Fo a value of capacitance consistent with the substituted values, including units 3 C = 3.3 1 F Altenate solution Altenate points Fo any statement of the equation elating capacitance, chage, and voltage C = Q V Fo an equation elating cuent and chage i = dq dt O Q = i dt Fo evaluating the integal Q = i dt, including clealy identifying the limits of integation Fo example, Q 6 ε t t 6 e dt ( ) e ( )( e 6 e ) = =.1 =. =.31 C The value of Q and the potential diffeence associated with the time inteval used in the integal ae then substituted into the fist equation. Using the above example, the associated voltage would be 3 1 V (.5 A)( 1 Ω ) = 9 V, and the capacitance would be 3. 1 F. Fo a value of capacitance consistent with the esult of the integation and the coect voltage diffeence fo that time inteval, including units (d) points Fo coectly labeling the capacito, esisto, battey, and the A and B switch elements Fo a cicuit that has the esisto, capacito, and battey connected in seies when the switch is closed at A, and will chage the capacito to 1 V Fo a cicuit that has the esisto and capacito connected in seies when the switch is closed at B, and will dischage the capacito fom 1 V to zeo Fo a voltmete connected in paallel acoss the capacito Copyight 3 by College Entance Examination Boad. All ights eseved. Available at apcental.collegeboad.com. 6
AP PHYSICS C: ELECTICITY AND MAGNETISM 3 SCOING GUIDELINES Question 3 15 points total Distibution (a) points Fo an aow downwad on o nea antenna Fo one coect justification statement Examples: F= qv B, the ight-hand ule, (noth down) = east, the left-hand ule fo electons (b) 5 points An equilibium is eached when the electic foce due to the sepaation of chage in the antenna balances the magnetic foce on an electon Fo a coect expession fo the magnetic foce, showing a coss poduct o an angula dependence Fo a coect expession fo the electic foce Equating the electic and magnetic foces: qe= qv B E = KBsin G Fo substitution of sin 55 Fo substitution of othe given values 5 E = KBsinG = ( 75 m s)( 6 1 T) sin 55 Fo the coect answe E =.37 V m (o NC) (c) points Using the elationship between electic field and potential diffeence fo the linea situation: V = Ed Fo substitution of the value of E fom pat (b) Fo substitution of the coect length, 15 m V =.37 V m 15 m ( )( ) V =.553 V An altenate method is to do pat (c) fist, using pinciples noted in pat (b), then substituting V into the elationship V = Ed to obtain E. Points equivalent to those above wee awaded fo this method. Copyight 3 by College Entance Examination Boad. All ights eseved. Available at apcental.collegeboad.com. 7
AP PHYSICS C: ELECTICITY AND MAGNETISM 3 SCOING GUIDELINES (d) Question 3 (cont d.) Distibution Fo indicating that the top of the wing is at the highe potential Note: To ean cedit, this answe must be consistent with the student's answe to pat (a). (e) 5 points i. () Fo indicating that thee must be a change in the magnetic flux though the closed loop Fo specifying a coect change in the plane's oientation o the connected wie that could esult in a change in flux though the closed loop. points ii. ( points) Fo any indication of the position of the connected wie in the closed loop Fo showing the coect diection of the esulting induced cuent on the diagam, based upon the conditions indicated in pat (e) i. Examples Ex. 1: The connecting wie tails behind the antenna, ove the body of the plane. The plane goes into a fowad dive, inceasing its angle with espect to hoizontal. The fowad dive would decease magnetic flux downwad though the loop, so a cuent will be induced to ceate an inceased downwad flux. Copyight 3 by College Entance Examination Boad. All ights eseved. Available at apcental.collegeboad.com. 8
AP PHYSICS C: ELECTICITY AND MAGNETISM 3 SCOING GUIDELINES Question 3 (cont d.) Distibution (e) (continued) Ex. : The connecting wie loops unde the wing, diectly unde the antenna. The plane makes a level ight tun. The tun will decease the nothwad component of magnetic flux though the loop, so a cuent will be induced to ceate an inceased flux to the noth. Othe acceptable concepts wee aanging the loop so its aea can be changed, o shielding a pat of the cicuit fom the magnetic field. Copyight 3 by College Entance Examination Boad. All ights eseved. Available at apcental.collegeboad.com. 9