AP PHYSICS C: ELECTRICITY AND MAGNETISM 2015 SCORING GUIDELINES

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1 AP PHYSICS C: ELECTRICITY AND MAGNETISM 2015 SCORING GUIDELINES Qustion 1 15 points total Distribution of points (a) i. For at last on arrow btwn th plats pointing downward from th positiv plats toward th ngativ plat and no xtranous arrows pointing in any othr dirction ii. For drawing an appropriat Gaussian surfac (nclosing at last th innr dg of on of th plats) that can b usd to dtrmin th lctric fild btwn th plats iii. 3 points For using a corrct statmnt of Gauss s law Q E da= Ú 0 For applying Gauss s law, using an nclosd charg and surfac ara consistnt with th surfac drawn in part (a)-ii qnc E( A ) = ( A GS is th ara of th nd of th Gaussian surfac btwn th GS 0 plats) qnc qnc E = Ê using s = ˆ 0 AGS Ë AGS s Q E = ( using s = ) 0 A For a corrct answr with work shown E = Q A Th Collg Board.

2 AP PHYSICS C: ELECTRICITY AND MAGNETISM 2015 SCORING GUIDELINES (b) Qustion 1 (continud) Distribution of points Comparing th quation for lctric fild btwn paralll plats to th givn quation: Q Q E = = k xd 0A - 0k0 A For an answr consistnt with part (a)-iii k = k x D 0 (c) i. Using th quation rlating th lctric fild to potntial diffrnc dv E =- dx For a corrct diffrntial quation dv Ê Q ˆ =- - dx Ë Á A -xd 0k0 dv Q = dx -xd 0k0 A Altrnat Solution: Using th quation rlating th lctric fild to potntial diffrnc: D V =-ÚE dr For a corrct diffrntial quation Q DV =-Ú - dx -xd 0k0 A Q DV = Ú dx -xd k A 0 0 Altrnat Point 2015 Th Collg Board.

3 AP PHYSICS C: ELECTRICITY AND MAGNETISM 2015 SCORING GUIDELINES (c) ii. (continud) 4 points Qustion 1 (continud) Distribution of points Sparating th variabls in th diffrntial quation from part (c)(i): dv Q = dx xd k A Q xd dv = Ê ˆ dx Ë 0k0A For using th corrct limits of intgration in attmpting to intgrat th quation abov VD D Q xd dv Ê ˆ Ú = dx Ë k A Ú V For corrctly intgrating th quation VD Q xd D [ V] V = Ê ˆÈ D 0 Ë k A Î QD DD 0 ( VD - V0 ) = Ê ˆ( - ) Ë 0k0A For an xprssion that givs th corrct absolut valu of th potntial diffrnc btwn th plats For having th potntial diffrnc b positiv QD DV = Ê ˆ ( -1) Ë0k0A D V 1.72QD = k A 0 0 (d) Using th quation for capacitanc: Q Q C = = DV Ê QD ˆ ( - 1) Ë0k0A For an answr consistnt with part (c)-ii 0k0A C = D ( - 1) 0k0A C = 1.72D 2015 Th Collg Board.

4 AP PHYSICS C: ELECTRICITY AND MAGNETISM 2015 SCORING GUIDELINES () 3 points Qustion 1 (continud) Distribution of points For slcting UV > U C For corrctly comparing th capacitanc or th potntial diffrnc with th varying dilctric constant to th capacitanc or th potntial diffrnc with th uniform dilctric constant For corrctly comparing th two stord nrgis consistnt with th comparison of th capacitancs or potntial diffrncs Exampl: According to th quation from part (d), CC > CV. Sinc U charg stord on th two capacitors is th sam, thn UV > UC. 2 Q =, if th 2C 2015 Th Collg Board.

14 AP PHYSICS C: ELECTRICITY AND MAGNETISM 2015 SCORING COMMENTARY Qustion 1 Ovrviw This qustion assssd studnts' undrstanding of Gauss's law, dilctrics, and nrgy storag in capacitors. Th dilctric constant varid with hight, and calculus was rquird. Whil rlativly straightforward, th problm challngd studnts in an unfamiliar way. Sampl: E&MQ1 A Scor: 15 Part (a)(i) and (ii) of this rspons arnd a total of 2 points for clar drawings of th lctric fild and Gaussian surfac. Part (a)(iii) arnd all 3 points for th us of Gauss s law in a dtaild solution consistnt with th drawing in part (a)(ii). Part (b) arnd for stating a corrct xprssion. Part (c)(i) arnd 1 point for stating a corrct quation that can b usd to find th potntial diffrnc btwn th plats, rgardlss of th sign. Part (c)(ii) arnd all 4 points for a dtaild valuation of th intgral that ld to a corrct positiv answr. Part (d) arnd for stating a corrct answr consistnt with part (c)(ii). Part () arnd all 3 points for a corrct answr slction and statmnt that compard th capacitanc and nrgy stord in ach capacitor. Sampl: E&MQ1 B Scor: 12 Part (a)(i) and (ii) of this rspons arnd a total of 2 points for clar drawings of th lctric fild and Gaussian surfac. Part (a)(iii) arnd all 3 points for th us of Gauss s Law in a dtaild solution consistnt with th drawing in part (a)(ii). Part (b) arnd for stating a corrct xprssion. Part (c)(i) arnd 1 point for stating a corrct quation that can b usd to find th potntial diffrnc btwn th plats, rgardlss of th sign. Part (c)(ii) arnd all 4 points for a dtaild valuation of th intgral that ld to a corrct positiv answr. Part (d) arnd for stating a corrct answr consistnt with part (c)(ii). Part () arnd no crdit sinc th incorrct answr is slctd, and thr ar no statmnts comparing th capacitanc or nrgy for ach cas. Sampl: E&MQ1 C Scor: 6 Part (a)(i) of this rspons arnd for a corrct arrow drawn in btwn th plats. Part (a)(ii) arnd no crdit bcaus th Gaussian surfac that is drawn ncloss zro nt charg. Part (a)(iii) arnd just for th us of Gauss s law, sinc th solution uss an nclosd charg not consistnt with th surfac drawn in part (a)(ii) and has an incorrct answr. Part (b) arnd no points. Part (c)(i) arnd for stating a corrct quation that can b usd to find th potntial diffrnc btwn th plats, rgardlss of th sign. Part (c)(ii) arnd 2 points for th us of th corrct limits on th intgral and a positiv final answr. Part (d) arnd no crdit. Part () arnd for a corrct answr slction but no corrct statmnts rlativ to a justification ar includd Th Collg Board.

General Notes About 2007 AP Physics Scoring Guidelines

General Notes About 2007 AP Physics Scoring Guidelines AP PHYSICS C: ELECTRICITY AND MAGNETISM 2007 SCORING GUIDELINES Gnral Nots About 2007 AP Physics Scoring Guidlins 1. Th solutions contain th most common mthod of solving th fr-rspons qustions and th allocation