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Final

# PCS 211 Final: Chapter 25 Premium

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School
Department
Physics
Course
PCS 211
Professor
Alexandre Douplik
Semester
Winter

Description
• • pointhan▯e in PoForc=:=FEnqrgy by movinGravitatiFolrce25.1Photntial5iffectcecnodeltitlic Potentia B The The integral is called a on the path taken from . This is an essential property of conservative forces. : B A g ▯ ▯ U W = = mg F S ▯ ▯ Conservative Forces path integraS S = = q mg 0▯ ▯ AEB S • or adS ▯ ▯ U W B A line integra= = q ▯ F E l from0point E ▯ S 0 S = . q S A E and A S to elecrAcfied:ivalent un*Unit of popential: voltThe potentiaDefineerence: 1 V is the work required per un V s aitalar.otential energy per unit charge. potcatclla.te E from = Electric potential 1 C1 J Useful to V C N p = = m V ▯ ▯E P • ds : V= p it charge to bring a positive test . ▯ V ▯ 0 at = U/q 0q U ▯ = 0. ▯ A B E ds *Notice the difference between potential and potential energy.tial Di1etetcal.EieeUrnofV(flt(eltri)gaelrsy common energy unit: the energy Electricfiesieikimalunet.ergy increases, the potential energy decreases ▯ V = : Release a positive charge in a uniform field. BV 0 ▯ AV ▯ U = q = 10 ▯ -19 A B ways point to lower potential direction. C V =1.60 ▯ • V U ds = = q ▯ or loses by moving through a ▯ A B ▯ V E 10 = cos0 J19 q El ds = ▯ El Equipotential Surface lines.erpendichlerythheee.eIimiufsedtial is the is a surface on • • • • d=0.3cm kineIifcaneroynw|E|? WhiDhirsdtihaofhtheeerpotintfiiaell?d?its E Example: The electric field between two parallel plates = V B l V A = | 0.3 + + + + + + ▯ 12 10 V 2 m 12V = - ▯ - - - - - - 10 3 V m (This For multiplNote,Tntch,argeTherefFooePGenerally,e:tw(3)nFiointorant)D.defrerDera3uileceiitflledtines. Potential Energy Due to Point Charges ▯ V depends only on and point ▯ ˆ ▯ E ▯ V • V = V ▯ r = ds = k = B 0 atAand ▯ = ▯ re V . A▯Br ds A▯ B ˆq ▯ A r e cos e V B = ,not on the path. q A ▯ dr ▯ • = ds . Then = dr ds ▯ Br k AE B V q • r = B[1] ds k V ▯ ▯ = A 1 A A i r q k i i r q (b) Find the work re(a) Find V2.Pm3 a 3 -6xample: The potential Due to Two Point Charges W pV pV = = = 3q 8.99 ek ) ) pV ▯ ▯ ▯ xm4 C C = ▯ 1r 1 (3 10 + ▯ 9 2r 2 10 C Nm ▯ ▯ ▯ ▯ 2 2 C6 ▯ ▯▯2▯ )( ▯ ▯ m 10 6.29 ▯ C6 ▯ ▯ 10 6 V3 C charge from ) m 10 = 6 18.9 C ▯ ▯▯ ▯ ▯ 10 6.29 ▯ ▯ 3 to P. ▯ J 10 3 V Together: (b) Second, briThree Charges:n charge q fromEnerTgwoPotential Energy of a Charge Particle Systemd charge q must be done.f q to the system to bring the two charges near each other. ▯ q q to the point P without acceleration: 2< 0, the>0,
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