Electrc & Electrc Gravtatonal Increases as you move farther from Earth mgh Sprng Increases as you ncrease sprng extenson/comp resson Δ Increases or decreases as you move farther from the charge U ncreases as you get farther from Earth U0 Gravtatonal f Udecreases Earth mgh Speeds up so Kncreases U changes as you change r ncreases f K U0 Ue K f Ue f K Ug K f Ug f Slows down so Kdecreases sgns K Ue K f Ue f : Charge launcher K U g U sp U e W K U g U sp U e U0 Udecreases f Speeds up so Kncreases K Ue K f Ue f ncreases U0 f Slows down so Kdecreases Let y0 at launch level Cannon ball ntally not movng Cannon ball s now movng
Electrc potental energy Exercse 8.99 0!" $ Coulomb s constant permttvty constant 8.99 0!" $ 8.85 0 & $ " Is the change U of the partcle postve, negatve, or zero as t moves from the ntal locaton, to the fnal locaton, f? HINT: ' ( )* *, Copyrght 2007, Pearson Educaton, Inc., Publshng as Pearson AddsonWesley. Electrc Electrc & Electrc ' ( )* *, ' ( 3 *, 2 * *,./0 2 V )* 2 2 Suppose that the heart's dpole charges Q and Q are separated by dstance d. Wrte an expresson for the V feld due to both charges at pont A, a dstance d to the rght of the Q charge. 2 6&,89 ; 2? 2 6@,89 ;? Add: 2 89 ; &BC @BC BC D D D 2
dfference Change n Electrc The value of the electrc potental depends on the choce of zero level, so we often use the dfference n electrc potental between two ponts. Meters measure only ΔV V0 s a practcal mpossblty to determne so we have assumed V0 locatons n crcuts, called the ground. 2 BC EF C GH BC EF C GH I J I K 2 2 Δ Δ2 Checkng Understandng Equpotental Lnes (surfaces) & Electrc Feld Lnes Rank n order, from largest to smallest, the electrc potentals at the numbered ponts. HINT: 3 ( )* LM Copyrght 2007, Pearson Educaton, Inc., Publshng as Pearson AddsonWesley. Equpotental surfaces: Representng the V feld The lnes represent surfaces of constant electrc potental V, called equpotental surfaces. The surfaces are spheres (they look lke crcles on a twodmensonal page). Contour maps: An analogy for equpotental surfaces V )* 20 Pearson Educaton, Inc. 3
A Topographc Map Graphcal Representatons of Electrc Δ Δ2 Connectng and Feld and Feld for Three Important Cases The Insde a ParallelPlate Capactor Solvng Problems NOPQR Δ2 Δ Slope E
A proton has a speed of 3.5 x 0 5 m/s at a pont where the electrcal potental s 600 V. It moves through a pont where the electrc potental s 000 V. What s ts speed at ths second pont? Its about! How do A proton s released from rest at pont a. It then travels past pont b. What s ts speed at pont b? Its about! How do Δ Δ2 Δ Δ2 Copyrght 2007, Pearson Educaton, Inc., Publshng as Pearson AddsonWesley. Copyrght 2007, Pearson Educaton, Inc., Publshng as Pearson AddsonWesley. (How s ths smlar to the prevous problem?) A proton has a speed of 3.5 x 0 5 m/s at a pont where the electrcal potental s 600 V. It moves through a pont where the electrc potental s 000 V. What s ts speed at ths second pont? Its about! How do : (How s ths smlar to the prevous problems?) A parallelplate capactor s held at a potental dfference of 250 V. A proton s fred toward a small hole n the negatve plate wth a speed of 3.0 x 0 5 m/s. What s ts speed when t emerges through the hole n the postve plate? (Hnt: The electrc potental outsde of a parallelplate capactor s zero). Δ Δ2 Copyrght 2007, Pearson Educaton, Inc., Publshng as Pearson AddsonWesley. For the stuaton shown n the fgure, fnd A. The potental at ponts a and b.the potental dfference between a and b. B. The potental energy of a proton at a and b. C. The speed at pont b of a proton that was movng to the rght at pont a wth a speed of.0 x 0 5 m/s. D. The speed at pont a of a proton that was movng to the left at pont b wth a speed of.0 x 0 5 m/s. Source charges create the electrc potental shown. A. What s the potental at pont A? At whch pont, A, B, or C, does the electrc feld have ts largest magntude? B. Is the magntude of the electrc feld at A greater than, equal to, or less than at pont D? C. What s the approxmate magntude of the electrc feld at pont C? D. What s the approxmate drecton of the electrc feld at pont C? 5