Download 7.9.1 Electric Potential Energy

7.9.1ElectricPotentialEnergy
Achargedobjectinanelectricfieldhaspotentialenergy.Potentialenergyisa
scalarquantity.Ifwemoveapositivelychargedobjecttowardsanother
positivelychargedobject,theyrepel.Workisdoneinbringingonecharge
towardsanother.Theworkthatisdoneisstoredaselectricpotentialenergy.The
potentialenergyisdefinedtobezerowhentheobjectsareinfinitelyfarapart
andincreasinglypositiveastheyarebroughttogether.
Letusconsidertwopointpositivecharges:
ThefirstpointpositivechargeQcreatesaradialelectric
fieldEwhichvariesaccordingtotheexpressionwesaw
inthepreviousunit(7.8):
1 𝑄
𝐸
=
+
4𝜋𝜀' 𝑟 *
F Thesecondpointpositivecharge𝑞,feelsarepulsiveforceFinthisfield:
1 𝑄𝑞
𝐹 = 𝑞𝐸 =
4𝜋𝜀' 𝑟 *
Lookawaynowifyoudon’tliketrickymaths!Note:notinsyllabus.
<
< 9
34
9 34
workdone=forcexdistance=∫: 𝐹𝑑𝑟 = 567 ∫: : ; 𝑑𝑟 = 567 : 8
8
So,thepotentialenergy(𝐸-./ )of𝑞atadistancerfromQisgivenby:
1 𝑄𝑞
𝐸-./ =
4𝜋𝜀' 𝑟
!Calculatetheelectricpotentialenergyofapointchargeq=+3.0Catadistanceof
0.4mfromapointchargeQ=+10.0C.
Unlikegravitationalpotentialenergy,whichisnegativeeverywhere,electrical
potentialenergycanbepositiveornegative.Anegativepotentialenergyoccurs
forunlikecharges.
!Calculatetheelectricpotentialenergyofapointchargeq=-1.0Catadistanceof
0.2mfromapointchargeQ=+5.0C.
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Electricpotentialenergyisadditive.Thismeansthatwhenwehavemorethan
onechargeproducingelectricfields,youjustnumericallyaddtogetherthe
differentcontributions.
Considerthefollowingsituation:
Ifwewanttoworkoutthe
d1
potentialenergyofqlocated
+ q
+
Q1
atadistanced1fromQ1and
distanced2fromQ2,wejust
workouttheindividual
d2
contributionsandaddthem
together.Note,thatQ2isa
negativecharge,sowill
Q2 -
produceanegativepotential
energy.
!Calculatetheelectricpotentialenergyforachargeq=+2.0Cinthediagram
above,whereQ1=+5.0C,Q2=-10C,d1=10cm,d2=8cm.
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