Lect02 - Physics 212 Le cture2 Today's C pt: once TheEle...

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Unformatted text preview: Physics 212 Le cture2 Today's C pt: once TheEle ctric Fie ld C ontinuous C hargeDistributions 50 40 30 20 10 0 Confused Avg = 3.43 Confident Physics 212 Le cture2, S 1 lide Music Oscar Peterson Kenny Barron Dave Brubeck Thelonius Monk Marcus Roberts BB Who is the Artist? A) B) C) D) E) Why? I gue I 'min a classic m ss ood.. Most uniquepiano playe r?? Che out theJazz Biography C (couldn't find a picture gre ck D ) at re cordings from40's and 50's Physics 212 Lecture 2, Slide 2 C oulom Law (fromlast tim ) b's e I f the arem than two charge pre nt, thetotal forceon any give chargeis re ore s se n just theve sumof theforce dueto e of theothe charge ctor s ach r s: q2 F4,1 F4,1 q2 q1 F 1 F2,1 F q1 F3,1 F2,1 F3,1 F F2,1 1 q4 F3,1 1 q4 F F2,1 1 q3 q3 +q1 -> -q1 dire ction re rse ve d F3,1 F4,1 F4,1 r kq1q2 kq1q3 kq1q4 ^ ^ ^ F1 = 2 r12 + 2 r13 + 2 r14 r12 r13 r14 33 MATH: r kq3 F1 kq2 kq4 ^ ^ ^ = 2 r12 + 2 r13 + 2 r14 q1 r12 r13 r14 Physics 212 Le cture2, S 3 lide Ele ctric Fie ld Thee ctric fie E at a point in space is defined as le ld the force per unit charge at that point. r r F Ek q Electric field due to a point charged particle r Q ^ E=k 2r r q2 E4 E2 Superposition r E= i Qi ^ k 2 ri ri E Field points toward negative and Away from positive charges. q3 08 E3 q4 Physics 212 Lecture 2, Slide 4 Pre flight 4) B? 100 80 60 40 20 0 "B is close to -Q than to +Q, so thee ct of -Q's charge r ffe will begre r than +Q. S B is positive it will m to ate ince , ove thele dueto theattractiveforceof -Q on it." ft Great! Nailed It !! Physics 212 Lecture 2, Slide 5 10 BB Pre flight A B C D 70 60 50 40 30 20 10 0 "By C oulom Law, theforceby +Q on q is (kQq)/r^2. The b's forceby +2Q on q is (kQq)/2r^2. S both force arepushing ince s in oppositedire ctions, the havediffe nt signs. Theforceby y re +Q pre vails, so q will m to theright in thedire ove ction of that force ." left right stay still Physics 212 Lecture 2, Slide 6 12 Pre flight "The two equal charges are the same distance away from point A, thus they will cancel out and will be a charge of zero." WHAT'SWRONG WI TH THI SEXPLANATI ON ?? 09 Physics 212 Lecture 2, Slide 7 "The two equal charges are the same distance away from point A, thus they will cancel out and will be a charge of zero." r r Q E=k 2 r Q E+ = + k 2 r Q E- = - k 2 r VEC TORSVEC TORSVECTORS ALWAYSDRAW A PICTURE FIRS !! T r E+ E = E+ + E- = 0 r E r E- 09 r r r E = E+ + E- 0 Physics 212 Le cture2, S 8 lide Pre flight 80 60 40 "Thene forcere ains thesam be t m e causethelaw of supe rposition in both case cause them s s agnitudeof thee ctric le fie to re ain thesam . Theonly diffe nceis in the ld m e re dire ction." 20 0 12 1 2 Same Physics 212 Le cture2, S 9 lide BB Two Charge s Two charge q1 and q2 arefixe at points (-a,0) and (a,0) as shown. Toge r s d the the producean e ctric fie at point (0,d) which is dire d along thene y le ld cte gativeyaxis. y (0,d) r E q1 (-a,0) q2 (a,0) x Which of thefollowing state e is true m nts : a) b) c) d) 22 Both charge arene s gative Both charge arepositive s Thecharge areopposite s The is not e re nough inform ation to te how thecharge are ll s re d late Physics 212 Lecture 2, Slide 10 - - + + + 23 Physics 212 Le cture2, S 11 lide BB Exam ple "I would hope for more example calculations involving Coulomb's law and electric field strength." d -q d +q +q P alculateE at point P. C r E= i Qi ^ k 2 ri ri 20 Physics 212 Lecture 2, Slide 12 C ontinuous C hargeDistributions "What theinte grals haveto do with theforceof thee ctric fie Aretheinte le ld... grals actually ne ssary for unde ce rstanding this? " YOU BETC ! HA S m um ation be e an inte (becare with ve nature com s gral ful ctor ) S m try is ofte he ym e n lpful Line chargede ar nsity is ofte use n ful =Q/L dq = dx r E= i Qi ^ k 2 ri ri r dq ^ E= k 2 r r Physics 212 Le cture2, S 13 lide C hargeDe nsity "What is ?? " BB ar oulom e r bs/m te Line (=Q/L) C urface( = Q/A) C oulom e r2 bs/m te S e oulom e r3 bs/m te Volum ( = Q/ V) C om om try S eGe e phe S re ylinde r C 4 V = r 3 A = 4 r 2 3 V = r 2 L A = 2 rL What has m ne charge ore t ?. A) B) A sphe w/ radius 2 m te and volum chargede re e rs e nsity = 2 C 3 /m A sphe w/ radius 2 m te and surfacechargede re e rs nsity = 2 C 2 /m C) Both A) and B) havethesam ne charge e t . 28 Physics 212 Lecture 2, Slide 14 Pre flight 100 80 60 40 20 0 "The field vectors cancel out for point A, but add together for point B." 29 Physics 212 Lecture 2, Slide 15 ACT BB 31 Physics 212 Lecture 2, Slide 16 Straight Rod "REALLY REALLY TOUGH and COMPLI CATED ve rsions of calculating e ctric fie dueto m le lds ultiplefiniteline of s charge :) " s. BB y A rod carries a total charge of Q, uniformly distributed over its length. d What is the direction of E at the origin? x A) E=0 ------------ 45o d -Q B) E y -Q ------------ 45o C) E S m try ! ym e x 33 Physics 212 Lecture 2, Slide 17 Straight Rod + Q y -----a ------ 45o d -Q A rod carries a total charge of Q, uniformly distributed over its length and a point charge Q is located as shown. d What is the direction of E at the origin? a -Q x A) E=0 B) E C) E There is no exact cancellation here ! The point charge Q is at a distance a from origin The rod has some charge that is > distance a from origin 35 Physics 212 Lecture 2, Slide 18 y Arc Rod + Q An arc carries a total charge of Q, uniformly distributed over its length and a point charge Q is located as shown -Q a a -Q What is the direction of E at the origin? A) E = 0 x B) E C) E There is no exact cancellation here ! The point charge Q is at a distance a from origin The arc has all its charge at a distance a from origin However, most of arc charge gives rise to field not along 45o line !! 40 Physics 212 Lecture 2, Slide 19 Arc Rod + Q "I would like it if the professor deals more with the integrals of electric fields practices. =)" y +Q a An arc carries a total charge of +Q, uniformly distributed over its length and a point charge Q is located as shown dE What is ? How is dq related to d? What is dEx for any ? Calculate Ex at the origin! x = Q 2Q = a a 2 dq = ds = ad dE x = k dq sin 2 a dq = 2Q d 2k Q dE x = sin d 2 a 2k Q Ex = a2 /2 sin d = 0 2k Q a2 Physics 212 Lecture 2, Slide 20 Note s Pre flight + Pre cture3 dueby 6:00 AM Tue le sday Hom work 1 is dueThursday S p 3rd e e Labs start August 31st Discussion Quiz ne we k will beon C xt e oulom Law and E b's Hom work 2 is dueTue e sday S pte be 8th (6:00 AM) e m r Physics 212 Lecture 2, Slide 21 ...
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This note was uploaded on 03/05/2011 for the course PHYS 212 taught by Professor Kim during the Spring '08 term at University of Illinois, Urbana Champaign.

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