Download PHY112 – Chapter 15 – Problems – Electric Forces and Electric

PHY112–Chapter15–Problems–ElectricForcesandElectricFields
1.A7.50-nCchargeislocated1.80mfroma4.20-nCcharge.(a)Findthemagnitudeoftheelectrostaticforcethatone
particleexertsontheother.(b)Istheforceattractiveorrepulsive?
4.Asmallsphereofmassm=7.50gandchargeq1=32.0nCisattachedtotheendofastringandhangsvertically,as
showinthefigurebelow.Asecondchargeofequalmassandchargeq2=–58.0nCislocatedbelowthefirstchargea
distance d = 2.00 cm below the first charge. (a) Find the tension in the string. (b) If the string can withstand a
maximumtensionof0.180N,whatisthesmallestvaluedcanhavebeforethestringbreaks?
5.Thenucleusof 8Be,whichconsistsof4protonsand4neutrons,isveryunstableandspontaneouslybreaksintotwo
alpha particles (helium nuclei, each consisting of 2 protons and 2 neutrons). (a) What is the force between the two
alphaparticleswhentheyare5.00x10-15mapart,and(b)whatistheinitialmagnitudeoftheaccelerationofthealpha
particlesduetothisforce?Notethatthemassofanalphaparticleis4.0026u(u=massofasingleproton).
8.Fourpointchargesareatthecornersofasquareofsidea,asshownbelow.Determinethemagnitudeanddirection
oftheresultantelectricforceonq,withke,q,andaleftinsymbolicform.
9. Two small identical conducting spheres are placed with their centers 0.30 m apart. One is given a charge of
12x10-9C,theotherachargeof–18x10-9C.(a)Findtheelectrostaticforceexertedononespherebytheother.(b)
The spheres are connected by a conducting wire. Find the electrostatic force between the two after equilibrium is
reached,wherebothsphereshavethesamecharge.
10.CalculatethemagnitudeanddirectionoftheCoulombforceoneachofthethreechargesshownbelow.
11.Threechargesarearrangedasshownbelow.Findthemagnitudeanddirectionoftheelectrostaticforceonthe
chargeattheorigin.
13.Threepointchargesarelocatedatthecornersofanequilateraltriangle,asinthefigurebelow.Findthemagnitude
anddirectionofthenetelectricforceonthe2.00μCcharge.
15.Twosmallmetallicspheres,eachofmassm=0.20g,aresuspendedaspendulumsbylightstringsfromacommon
point,asshownbelow.Thespheresaregiventhesameelectriccharge,anditisfoundthattheycometoequilibrium
wheneachstringisatanangleofθ=5.00withthevertical.IfeachstringhaslengthL=30.0cm,whatisthemagnitude
ofthechargeoneachsphere?
16.ParticleAofcharge3.00x10-4Cisattheorigin,particleBofcharge–6.00x10-4Cisat(4.00m,0),andparticleCof
charge1.00x10-4Cisat(0,3.00m).(a)Whatisthex-componentoftheelectricforceexertedbyAonC?(b)Whatis
they-componentoftheforceexertedbyAonC?(c)FindthemagnitudeoftheforceexertedbyBonC.(d)Calculate
thex-componentoftheforceexertedbyBonC.(e)Calculatethey-componentoftheforceexertedbyBonC.(f)Sum
thetwox-componentstoobtaintheresultantx-componentoftheelectricforceactingonC.(g)Repeatpart(f)forthe
y-component.(h)FindthemagnitudeanddirectionoftheresultantelectricforceactingonC.
17.Asmallobjectofmass3.80gandcharge–18μCissuspendedmotionlessabovethegroundwhenimmersedina
uniformelectricfieldperpendiculartotheground.Whatisthemagnitudeanddirectionoftheelectricfield?
18.(a)Determinetheelectricfieldstrengthatapoint1.00cmtotheleftofthemiddlechargeshownbelow.(b)Ifa
chargeof–2.00μCisplacedatthispoint,whatarethemagnitudeanddirectionoftheforceonit?
19. An electric field of magnitude 5.25 x 105 N/C points due south at a certain location. Find the magnitude and
directionoftheforceona–6μCchargeatthislocation.
20. An electron is accelerated by a constant electric field of magnitude 300 N/C. (a) Find the acceleration of the
electron. (b) Use the equations of motion with constant acceleration to find the electron’s speed after 1.00 x 10-8 s,
assumingitstartsfromrest.
21.AsmallblockofmassmandchargeQisplacedonaninsulated,frictionless,inclinedplaneofangleθ,asinthe
figurebelow.Anelectricfieldisappliedparalleltotheincline.(a)Findanexpressionforthemagnitudeoftheelectric
fieldthatenablestheblocktoremainatrest.(b)Ifm=5.40g,Q=–7.00μC,andθ=25.00,determinethemagnitude
anddirectionoftheelectricfieldthatenablestheblocktoremainatrestontheincline.
22.Asmallsphereofchargeq=+68μCandmassm=5.8gisattachedtoalightstringandplacedinauniformelectric
fieldEthatmakesanangleθ=370withthehorizontal.Theoppositeendofthestringisattachedtoawallandthe
sphereisinstaticequilibriumwhenthestringishorizontal,asshownbelow.(a)Constructafreebodydiagramforthe
sphere.Find(b)themagnitudeoftheelectricfieldand(c)thetensioninthestring.
23.Aprotonacceleratesfromrestinauniformelectricfieldof640N/C.Atsomelatertime,itsspeedis1.20x106
m/s. (a) Find the magnitude of the acceleration of the proton. (b) How long does it take the proton to reach this
speed?(c)Howfarhasitmovedinthatinterval?(d)Whatisitskineticenergyatthelatertime?
25. Two equal positive charges are at opposite corners of a trapezoid, as in the figure below. Find symbolic
expressionsforthecomponentsoftheelectricfieldatthepointP.
26. Three point charges are located on a circular arc, as shown below. (a) What is the total electric field at P, the
centerofthearc?(b)Findtheelectricforcethatwouldbeexertedona–5.00nCchargeplacedatP.
27.Inthefigurebelow,determinethepoint(otherthaninfinity)atwhichthetotalelectricfieldiszero.
28.Threechargesareatthecornersofanequilateraltriangle,asshownbelow.Calculatetheelectricfieldatapoint
midwaybetweenthetwochargesonthex-axis.
29.Threeidenticalcharges(q=–5.0μC)liealongacircleofradius2.0matanglesof300,1500,and2700,asshownin
thefigurebelow.Whatistheresultantelectricfieldatthecenterofthecircle?
40.AuniformelectricfieldofmagnitudeE=435N/Cmakesanangleofθ=65.00withaplanesurfaceofareaA=3.50
m2shownbelow.Findtheelectricfluxthroughthissurface.
41.Anelectricfieldofintensity3.50kN/Cisappliedalongthex-axis.Calculatetheelectricfluxthrougharectangular
plane0.350mwideand0.700mlongif(a)theplaneisparalleltotheyz-plane,(b)theplaneisparalleltothexy-plane,
and(c)theplanecontainsthey-axisanditsnormalmakesanangleof40.00withthex-axis.
52.Asmallplasticballofmassm=2.00gissuspendedbyastringoflengthL=20.0cminauniformelectricfield,as
indicatedbelow(left).Iftheballisinequilibriumwhenthestringmakesaθ=15.00anglewiththevertical,whatisthe
netchargeontheball?
57.Two2.0-gspheresaresuspendedby10.0-cmlonglightstrings,shownabove(right).Auniformelectricfieldis
appliedinthex-direction.Ifthesphereshavechargesof–5.0x10-8Cand+5.0x10-8C,determinetheelectricfield
intensitythatenablesthespherestobeinequilibriumatθ=100.