5B_-002ElectricPotentialEnergywithMultipleCharges
PROMPTSAFTER
STATEMENTOFTHEPROBLEM:ElectricPotentialEnergywithMultipleCharges
Three3×10!! Cchargesarearrangedasshown.Ifafourth3×10!! Cchargeismovedtothe
location𝑟 = [3 cm, 4 cm],whatisitspotentialenergyduetoitspresenceneartheother
charges?
STRATEGY
Thethreeoriginalchargescombinetocreateanelectric
potential(voltage)atthelocationofinterest.Acharge
placedatthatlocationwillhavethepotentialenergy
𝑈 = 𝑞𝑉.Inthecaseofthefourchargeconfiguration,each
chargehaspotentialenergyduetothevoltagecreatedbythe
otherthreecharges.Thenetpotentialenergystoredinthis
chargeconfiguration,alsocalledelectrostaticpotential
energy,isthesumoftheindividualpotentialenergies.
IMPLEMENTATION
Use∆𝑉=
!"!!
!!
y
qa +
ra
rb
qb
+
Place qt here
rc
+
qc
todeterminethevoltageatthelocationofinterest𝑟 = [3 cm, 4 cm] and
then𝑈 = 𝑞𝑉 todeterminetheelectrostaticpotentialenergyatthatpoint..
CALCULATION
∆𝑉!"# =
𝑘𝑞! 𝑘𝑞! 𝑘𝑞!
+
+
𝑟!
𝑟!
𝑟!
Withnumbers:
∆𝑉 = _____________________________________________________________________________________________
∆𝑉 = 2.2×10!! V
Thepotentialenergyofthefourthchargeisthen
∆𝑈 = 𝑞∆𝑉 = (_____________C)(___________________𝑉 = 6.5J
Inthespacesabove,supplythemissingnumbersasyouwouldentertheminyour
calculator,thencompletethecalculations
SELF-EXPLANATIONPROMPTS
1. Inpreviousexamplesthevoltageatalocationofinterestwasdeterminedasthe∆V
betweenthatlocationandinfinity.Inthecaseoftheelectricpotentialenergyofthe
chargeatthelocationofinterest,it,also,isthedifferenceinthepotentialenergy
betweenthatspotandsomereferencepoint.Whereisthatreferencepoint?
x
5B_-002ElectricPotentialEnergywithMultipleCharges
PROMPTSAFTER
2. Ifthevoltageatalocationofinterestwasduetoacontinuousdistributionofcharge,
howwouldtheelectricpotentialenergyofasinglechargeplacedatthatlocationbe
calculated?
3. Theauthorcalculatedthetotalpotentialduetothethreeinitialcharges,thenmultiplied
bythevalueofthefourthcharge.Wouldithavebeencorrect,instead,tocalculatethe
potentialenergyofthenewchargeduetothepotentialofoneoftheothers,repeatthat
calculationthreetimes,thensumtheresult?Whyorwhynot?
4. Thepotentialenergycalculatedisthepotentialenergyofafourthchargeaddedtothe
otherthree..Whatwouldweneedtodotocalculatethetotalpotentialenergyofallof
thecharges?(Hint:Thinkaboutbringinone,thenanother,thenanother…)
5. Adevicethathadmany,manylikechargesplacedonitincloseproximitycanpossessa
greatdealofelectrostaticenergy.Intermsofworkdonebyanoutsideagent,what
wouldthiselectrostaticpotentialenergyequal?
5B_-002ElectricPotentialEnergywithMultipleCharges
PROMPTSAFTER