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Electric Potential.Pdf ElectricElectric PotentialPotential AA PowerPointPowerPoint PresentationPresentation byby PaulPaul E.E. Tippens,Tippens, ProfessorProfessor ofof PhysicsPhysics SouthernSouthern PolytechnicPolytechnic StateState UniversityUniversity © 2007 Objectives:Objectives: AfterAfter completingcompleting thisthis module,module, youyou shouldshould bebe ableable to:to: • Understand an apply the concepts of electric potential energy, electric potential, and electric potential difference. • Calculate the work required to move a known charge from one point to another in an electric field created by point charges. • Write and apply relationships between the electric field, potential difference, and plate separation for parallel plates of equal and opposite charge. Review:Review: WorkWork andand EnergyEnergy WorkWork isis defineddefined asas thethe productproduct ofof displacementdisplacement dd andand aa parallelparallel appliedapplied forceforce F.F. WorkWork == Fd;Fd; Units:Units: 11 JJ == 11 NN mm PotentialPotential EnergyEnergy UU isis defineddefined asas thethe abilityability toto dodo workwork byby virtuevirtue ofof positionposition oror conditioncondition.. (Joules)(Joules) KineticKinetic EnergyEnergy KK isis defineddefined asas thethe abilityability toto dodo workwork byby virtuevirtue ofof motionmotion (velocity)(velocity).. (Also(Also inin joules)joules) SignsSigns forfor WorkWork andand EnergyEnergy WorkWork ((FdFd)) isis positivepositive ifif anan appliedapplied forceforce FF isis inin thethe samesame directiondirection asas thethe displacementdisplacement dd.. TheThe forceforce FF doesdoes positivepositive work.work. B F TheThe forceforce mgmg doesdoes negativenegative workwork. m d TheThe P.E.P.E. atat BB relativerelative toto AA isis mg positivepositive becausebecause thethe fieldfield cancan dodo A positivepositive workwork ifif mm isis released.released. P.E.P.E. atat AA relativerelative toto BB isis negativenegative;; outsideoutside forceforce neededneeded toto movemove mm.. GravitationalGravitational WorkWork andand EnergyEnergy Consider work against g to move m B from A to B, a vertical height h. F Work = Fh = mgh m h g At level B, the potential energy U is: mg A U = mgh (gravitational) The external force does positive work; the gravity g does negative work. TheThe externalexternal forceforce FF againstagainst thethe g-fieldg-field increasesincreases thethe potentialpotential energy.energy. IfIf releasedreleased thethe fieldfield givesgives workwork back.back. ElectricalElectrical WorkWork andand EnergyEnergy An external force F moves +q from A to B against the field force qE. B + + + + Work = Fd = (qE)d Fe d At level B, the potential energy U is: +q + qE E U = qEd (Electrical) A ---- The E-field does negative work; External force does positive work. TheThe externalexternal forceforce FF againstagainst thethe E-fieldE-field increasesincreases thethe potentialpotential energy.energy. IfIf releasedreleased thethe fieldfield givesgives workwork back.back. WorkWork andand NegativeNegative ChargesCharges Suppose a negative charge –q is moved against E from A to B. B + + + + Work by E = qEd qE d At A, the potential energy U is: -q E U = qEd (Electrical) A ---- No external force is required ! TheThe E-fieldE-field doesdoes positivepositive workwork onon –q–q decreasingdecreasing thethe potentialpotential energy.energy. IfIf releasedreleased fromfrom BB nothingnothing happens.happens. WorkWork toto MoveMove aa ChargeCharge Work to move +q from A to B. rb + + F kqQ + + F +Q + At A: a 2 ++ qE ra ra kqQ At B: Fb 2 rb kqQ Avg. Force: Favg Distance: ra -rb rrab kQq 11 Work Fd() r r Work kQq rr ab ab rrba AbsoluteAbsolute PotentialPotential EnergyEnergy AbsoluteAbsolute P.E.P.E. isis relativerelative toto r b ItIt isis workwork toto bringbring + ++ F +Q + +q from infinity to +++ qE +q from infinity to ra pointpoint nearnear QQ——i.e.,i.e., fromfrom toto rrb 0 11 11 kQq Work kQqWork kQq rrba rrbb Absolute Potential kQq U Energy: r ExampleExample 1.1. WhatWhat isis thethe potentialpotential energyenergy ifif aa +2+2 nCnC chargecharge movesmoves fromfrom toto pointpoint AA,, 88 cmcm awayaway fromfrom aa +6+6 CC charge?charge? TheThe P.E.P.E. willwill bebe positivepositive atat A pointpoint AA,, becausebecause thethe fieldfield cancan +2 nC dodo ++ workwork ifif qq isis released.released. 8 cm +Q PotentialPotential kQq U +6 C Energy:Energy: r (9 x 109-Nm2 )( 6 x 106- C)(+2 x 109 C) U C2 (0.08 m) UU == 1.351.35 mJmJ Positive potential energy SignsSigns forfor PotentialPotential EnergyEnergy ConsiderConsider PointsPoints A,A, B,B, andand C.C. A B ForFor +2+2 nCnC atat A:A: UU == +1.35+1.35 mJmJ 8 cm 12 cm Questions: +Q C 4 cm If +2 nC moves from A to B, +6 C does field E do + or – work? Moving Does P.E. increase or decrease? positive q +2 nC TheThe fieldfield EE doesdoes positivepositive work,work, thethe P.E.P.E. decreases.decreases. If +2 nC moves from A to C (closer to +Q), the field E does negative work and P.E. increases. ExampleExample 2.2. WhatWhat isis thethe changechange inin potentialpotential energyenergy ifif aa +2+2 nCnC chargecharge movesmoves fromfrom toto BB?? A B PotentialPotential kQq Energy:Energy: U r 8 cm 12 cm +Q From Ex-1: U = + 1.35 mJ A +6 C (9 x 199-Nm2 )( 6 x 106- C)(+2 x 109 C) U C2 0.900 mJ B (0.12 m) U = UB –UA = 0.9 mJ – 1.35 mJ UU == -0.450-0.450 mJmJ Note that P.E. has decreased as work is done by E. MovingMoving aa NegativeNegative ChargeCharge ConsiderConsider PointsPoints A,A, B,B, andand C.C. A B SupposeSuppose aa negativenegative --qq isis moved.moved. 8 cm 12 cm Questions: +Q C 4 cm If -q moves from A to B, does +6 C field E do + or – work? Does Moving P.E. increase or decrease? negative q - TheThe fieldfield EE doesdoes negativenegative work,work, thethe P.E.P.E. increases.increases. What happens if we move a –2 nC charge from A to B instead of a +2 nC charge. This example follows . ExampleExample 3.3. WhatWhat isis thethe changechange inin potentialpotential energyenergy ifif aa --22 nCnC chargecharge movesmoves fromfrom toto BB?? PotentialPotential kQq A B Energy:Energy: U r 8 cm 12 cm From Ex-1: UA = -1.35 mJ +Q (Negative(Negative duedue toto –– charge)charge) +6 C (9 x 199-Nm2 )(6 x 106- C)(-2 x 109 C) U C2 0.900 mJ B (0.12 m) UB –UA = -0.9 mJ – (-1.35 mJ) UU == +0.450+0.450 mJmJ AA –– chargecharge movedmoved awayaway fromfrom aa ++ chargecharge gainsgains P.E.P.E. PropertiesProperties ofof SpaceSpace Electric Field An electric field is a property of space allowing prediction of the . E force on a charge at that point. r F E ; FqE + + q +Q + +++ The field E exist independently of E is a Vector the charge q and is found from: kQ Electric Field: E r 2 ElectricElectric PotentialPotential ElectricElectric potentialpotential isis anotheranother propertyproperty ofof spacespace allowingallowing usus toto predictpredict thethe U P. V P.E.P.E. ofof anyany chargecharge qq atat aa point.point. q r ElectricElectric U + + VUqV; +Q + Potential:Potential: q +++ The units are: joulesjoules perper coulombcoulomb (J/C)(J/C) Potential ForFor example,example, ifif thethe potentialpotential isis 400400 J/CJ/C atat pointpoint PP,, aa ––22 nCnC chargecharge atat thatthat pointpoint wouldwould havehave P.E.P.E. :: U = qV = (-2 x 10-9C)(400 J/C); UU == -800-800 nJnJ TheThe SISI UnitUnit ofof PotentialPotential (Volt)(Volt) FromFrom thethe definitiondefinition ofof electricelectric potentialpotential asas P.E.P.E. perper unitunit chargecharge,, wewe seesee thatthat thethe unitunit mustmust bebe J/CJ/C.. WeWe redefineredefine thisthis unitunit asas thethe voltvolt (V).(V). U 1 joule V ; 1 volt = q 1 coulomb AA potentialpotential ofof oneone voltvolt atat aa givengiven pointpoint meansmeans thatthat aa chargecharge ofof oneone coulombcoulomb placedplaced atat thatthat pointpoint willwill experienceexperience aa potentialpotential energyenergy ofof oneone joulejoule.. CalculatingCalculating ElectricElectric PotentialPotential ElectricElectric PotentialPotential EnergyEnergy andand Potential:Potential: kQ P. V kQq U r UV; r rq + + +Q + kQq +++ SubstitutingSubstituting forfor r kQ V Potential U,U, wewe findfind V:V: qr kQ TheThe potentialpotential duedue toto aa positivepositive chargecharge isis V positive;positive; TheThe potentialpotential duedue toto aa negativenegative r chargecharge isis positive.positive. (Use(Use signsign ofof charge.)charge.) ExampleExample 4:4: FindFind thethe potentialpotential atat aa distancedistance ofof 66 cmcm fromfrom aa ––55 nCnC charge.charge. 9-Nm2 9 kQ 9 x 10C2 ( 5 x 10 C) P q = –4 C V . r (0.06 m) r 6 cm Negative V at - - - VVP == -750-750 VV - Q - Point P : P - - Q = -5 nC WhatWhat wouldwould bebe thethe P.E.P.E. ofof aa ––44 CC chargecharge placedplaced atat thisthis pointpoint P?P? UU == qVqV == ((--44 xx 1010-6 C)(C)(--750750 V);V); UU == 3.003.00 mJmJ SinceSince P.E.P.E. isis positive,positive, EE willwill dodo ++ workwork ifif qq isis released.released. PotentialPotential ForFor MultipleMultiple ChargesCharges TheThe ElectricElectric PotentialPotential VV inin thethe vicinityvicinity ofof aa numbernumber ofof chargescharges isis equalequal toto thethe algebraicalgebraic sumsum ofof thethe potentialspotentials duedue toto eacheach charge.charge. kQ12 kQ kQ3 r1 V Q1 - A A rrr123 r2 r3 + kQ Q3 - Q V 2 r PotentialPotential isis ++ oror –– basedbased onon signsign ofof thethe chargescharges Q.Q. ExampleExample 5:5: TwoTwo chargescharges QQ1= = +3+3 nCnC andand QQ2 == --55 nCnC areare separatedseparated byby 88 cmcm.. CalculateCalculate
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