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7.6ElectricFieldStrength
Anelectricfieldisaregionofspacewhereachargedobjectwillexperiencean
electrostaticforce.Theelectricfieldstrength(E)isthesizeoftheforce(F)feltby
aunitcharge:

= 
(1)!Fromthisequation,whatistheunitforelectricfieldstrengthE?
Uniformelectricfield
Wecancreateauniformelectricfieldbyapplyingapotentialdifferenceacross
twoparallelconductingplatesseparatedbyadistanced.Inthediagram,below,
fieldlinesaredrawntoshowtheelectricfield.
+V
+Q
d
F
0V
Fieldlinesshowtwothings.Thearrowsshowthedirectionaforcewillactona
positivechargeplacedatanyposition.Thespacingofthefieldlinestellsusabout
therelativestrengthofthefield.Thecloserthelinesaretogether,thestronger
thefield.
Ifwemovedacharge+Qfrom0Vto+V,wewouldneedtodoworkonthecharge
becausetheforceFwouldbeactingdownwards.
(2)!Writeanexpressionforworkdone(usingQ,E,d)inmovingthechargefrom
0Vto+V.(Hint:workdoneW=Fd)
(3)!TheworkdoneinmovingachargeQfrom0to+Visalsogivenby = .
SubstituteforWinyourfirstexpressionandsimplifytogetanexpressionforthe
electricfieldstrengthEforparallelplates.
(4)!Apotentialdifferenceof+100Visappliedacrosstwoparallelplateswitha
separationof1cm.Whatistheelectricfieldstrengthinthegap?
(5)!Whatistheforceona1.5x10-6Cchargeplacedinthegap?
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Considerthefollowingsituation:
+50V
 (
5mm
v
0V
(6)!Anelectron ( isfired,withvelocityv,intoagapbetweentwocharged
plates,5mmapart.Sketchthepaththeelectronwilltakeintheelectricfield.
Explainyouranswer.
(7)!Theelectronhasachargeof-1.6x10-19C.Whatforcewillitexperience?
(8)!Theelectronhasarestmassof9.11x10-31kg.Whataccelerationwillit
experience?
Radialelectricfield
ApointchargeQwillproducearadialelectricfieldstrengthgivenbythe
expression:
1 
=
4-  /
where- =permittivityoffreespace,r=radialdistancefromchargeQ.
(9)!Sketchagraphtoshowhowtheelectricfieldstrengthvarieswithdistancer
fromapointpositivecharge.Onthesamegraphdothesameforapointnegative
charge.
E
r
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Thediagram,left,showsfieldlinesarounda
negativepointcharge.
(10)!Whydothearrowspointinwards?
(11)!Howcanyoutellfromthefieldlinesthat
thestrengthoftheelectricfieldincreasesasyou
moveinwards?
TheforceexperiencebyachargeqisgivenbyF=qE
(12)!Showthattheforceexperiencedbyachargeqinaradialelectricfieldis
givenbytheexpression:
1 
=
4-  /
whereQisthepointchargeproducingtheradialfield.
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