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PHY132 Introduction to Physics IIClass 11 – Outline: Finishing Chapter26 on dipoles. Electric PotentialEnergy of:–Point Charges–Dipoles Electric Potential: V Voltage: ΔVQuickCheck 26.13Which dipole experiences no netforce in the electric field?A.A. Dipole A.B.B. Dipole B.C. Dipole C.D. Both dipoles A and C.C.E. All three dipoles.1

Dipoles in a Uniform Electric Field The figure shows anelectric dipole placed ina uniform externalelectric field. The net force on thedipole is zero. The electric field exerts atorque on the dipolewhich causes it to rotate.Dipoles in a Uniform Electric Field The figure shows anelectric dipole placed ina uniform externalelectric field. The torque causes thedipole to rotate until it isaligned with the electricfield, as shown. Notice that the positiveend of the dipole is inthe direction in which 𝐸points.2

QuickCheck 26.14Which dipole experiences no nettorque in the electric field?A.A. Dipole A.B.B. Dipole B.C. Dipole C.C.D. Both dipoles A and C.E. All three dipoles.Dipoles in a Uniform Electric Field The figure shows asample of permanentdipoles, such as watermolecules, in anexternal electric field. All the dipoles rotateuntil they are alignedwith the electric field. This is the mechanismby which the samplebecomes polarized.3

The Torque on a DipoleThe torque on a dipole placed in a uniform externalelectric field isDipoles in a Nonuniform Electric Field Suppose that a dipole isplaced in a nonuniformelectric field, such as thefield of a positive pointcharge. The first response of thedipole is to rotate until itis aligned with the field. Once the dipole is aligned, the leftward attractive forceon its negative end is slightly stronger than the rightwardrepulsive force on its positive end. This causes a net force to the left, toward the pointcharge.4

Dipoles in a Nonuniform Electric Field A dipole near a negativepoint charge is alsoattracted toward the pointcharge. The net force on a dipoleis toward the direction ofthe strongest field. Because field strength increases as you get closer toany finite-sized charged object, we can conclude thata dipole will experience a net force toward anycharged object.What is Potential Energy?A. mghB. When an object has the potential tospeed up.C. VoltageD. ½ k(Δx)25

Class 11 Preclass Quiz on MasteringPhysics 74% got: Two positive charges are equal. Charge A hasmore electric potential energy.Both of these charges have the potential to acceleratetoward the negative plate, speeding up.Class 11 Preclass Quiz on MasteringPhysics 70% of students got: The electric potential energy of asystem of two point charges is proportional to the inverse ofthe distance between the two charges.6

Class 11 Preclass Quiz on MasteringPhysics 49% of students got: A positive and a negative charge arereleased from rest in vacuum. They move toward each other.As they do a negative potential energy becomes morenegative.Class 11 Preclass Quiz on MasteringPhysics 56% of students got:“Dipole d has the smallest potential energy because it is alignedwith the electric field. The greater the angle between thepositive to the direction of the electric field, the greater theelectric potential.”7

Class 11 Preclass Quiz – Student Comments “If charged particle moves perpendicular to the electric fielddirection, does its potential not change then?” Harlow answer: Correct. If the charge movesperpendicular to the electric field, then the electric forcedoes zero work and the electric potential energy isunchanged. “for the equation of electric potential energy in a uniformfield, is the Uo always zero?”Uelec U0 qEs Harlow answer: No! U0 is arbitrary. You choose aconvenient value of s where U0 0. (similar to the zero-pointin gravitational potential energy.)Class 11 Preclass Quiz – Student Comments “What is the name of Sherlock Ohms' assistant.Dr.WATTSon!” “Q: What would you call a power failure? A: A current event.”8

Energy The kinetic energy of a system, K, is the sum of thekinetic energies Ki 1/2mivi2 of all the particles in thesystem. The potential energy of a system, U, is the interactionenergy of the system. The change in potential energy, U, is 1 times thework done by the interaction forces: If all of the forces involved are conservative forces(such as gravity or the electric force) then the totalenergy K U is conserved; it cannot be created ordestroyed.Work Done by a Constant Force Recall that the work done by a constant force dependson the angle between the force F and thedisplacement r. If 0 , then W F r. If 90 , then W 0. If 180 , then W F r.9

WorkIf the force is notconstant or thedisplacement isnot along a linearpath, we cancalculate the workby dividing thepath into manysmall segments.Electric Potential Energy in a Uniform Field A positive charge q inside acapacitor speeds up as it“falls” toward the negativeplate. There is a constant forceF qE in the direction of thedisplacement. The work done is:Welec qEsi qEsf The change in electricpotential energy is:ΔUelec WelecwhereUelec U0 qEs10

Electric Potential Energy in a Uniform FieldA positively chargedparticle gains kineticenergy as it moves inthe direction ofdecreasing potentialenergy.Electric Potential Energy in a Uniform FieldA negatively chargedparticle gains kineticenergy as it moves inthe direction ofdecreasing potentialenergy.11

Electric Potential Energy in a Uniform Field The figure showsthe energydiagram for apositively chargedparticle in auniform electricfield. The potentialenergy increaseslinearly withdistance, but thetotal mechanicalenergy Emech isfixed.QuickCheck 28.4A positive charge movesas shown. Its kineticenergyA. Increases.B. Remains constant.C. Decreases.12

The Potential Energy of Two Point Charges Consider two likecharges q1 and q2. The electric field of q1pushes q2 as it movesfrom xi to xf. The work done is: The change in electric potential energy of the systemis Uelec Welec if:The Potential Energy of Two Point ChargesConsider two point charges, q1 and q2, separated by aThe Potential Energy of Point Chargesdistance r. The electric potential energy is This is explicitly the energy of the system, not theenergy of just q1 or q2.Note that the potential energy of two chargedparticles approaches zero as r .13

The Potential Energy of Two Point Charges Two like chargesapproach each other. Their total energy isEmech 0. They gradually slowdown until the distanceseparating them is rmin. This is the distance ofclosest approach.The Potential Energy of Two Point Charges Two opposite charges areshot apart from oneanother with equal andopposite momenta. Their total energy isEmech 0. They gradually slow downuntil the distanceseparating them is rmax. This is their maximumseparation.14

The Potential Energy of Multiple Point ChargesThe Potential Energy of Multiple PointChargesmore than two point charges, the potentialConsiderenergy is the sum of the potential energies due to allpairs of charges:where rij is the distance between qi and qj.The summation contains the i j restriction to ensurethat each pair of charges is counted only once.Problem 28.37The four 1.0 g spheres shown inthe figure are releasedsimultaneously and allowed tomove away from each other.What is the speed of eachsphere when they are very farapart?15

The Potential Energy ofa Dipole Consider a dipole in auniform electric field. The forces F and F exert a torque on thedipole. The work done is: The change in electric potential energy of the systemis ΔUelec Welec if:16

The Potential Energy of a Dipole The potential energyof a dipole is 0 minimum atwhere the dipole isaligned with theelectric field. A frictionless dipolewith mechanicalenergy Emech willoscillate back andforth between turningpoints on either sideof 0 .The Electric Potential We define the electric potential V (or, for brevity, justthe potential) as This is NOT the same as electric potential energy.(different units, for one thing). The unit of electric potential is the joule per coulomb,which is called the volt V:17

QuickCheck 28.6A proton is releasedfrom rest at the dot.Afterward, the protonA. Remains at the dot.B. Moves upward with steadyspeed.C. Moves upward with an increasing speed.D. Moves downward with a steady speed.E. Moves downward with an increasing speed.Before Class 12 on Wednesday(my last class ) Please finish reading Knight Ch. 28 Please do the short pre-class quiz onMasteringPhysics by tomorrow night. Something to think about. A battery is designed tosupply a steady amount of which of the followingquantities?– Energy(Hint: only one ofthese is correct!)– Power– Electric potential difference– Electric current18