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30 Pages

### (31) Electric Fields

Course: PHYS 221, Fall 2007
School: Iowa State
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Word Count: 1226

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31 Electric Lecture Fields ACT: Two balls Two balls of equal mass are suspended from the ceiling with nonconducting wire. One ball is given a charge q and the other is given a charge 3q. Which of the following best represents the equilibrium position? 3q q q 3q 3q q A B C Same force on both (3rd law) and same mass! What is a &quot;field&quot;? Very basic definition: Assignment of a scalar or a...

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31 Electric Lecture Fields ACT: Two balls Two balls of equal mass are suspended from the ceiling with nonconducting wire. One ball is given a charge q and the other is given a charge 3q. Which of the following best represents the equilibrium position? 3q q q 3q 3q q A B C Same force on both (3rd law) and same mass! What is a "field"? Very basic definition: Assignment of a scalar or a vector to each point in space. Example of scalar field: Temperatures 7 7 73 72 71 82 84 83 75 68 64 80 73 82 88 55 66 88 75 80 88 83 90 91 92 77 The shown temperatures are samples of the field Example of vector field: Winds 77 73 72 71 82 84 83 88 75 77 68 64 80 73 57 56 55 66 80 88 75 90 83 92 91 The shown temperatures are samples of the field Electric field Definition: If the electric force on a test charge q located at point P is F, then the electric field at point P is: E F q Units: N/C Because the force is always proportional to q, the electric field is independent of the test charge! Electric field by a point charge The electric force by Q on q is F Q + q + E F Qq ^ k 2 r r Independent of q (test charge) Q + F q E The electric field by Q (source charge) is: E F q E Q ^ k 2r r Electric field by a negative/positive point charge + - If you place a test charge q near the source charge, you get a force. + q If you place a test charge q in a different place, you might get a different force. + q If the test charge is 2q, the force is twice as large: + 2q Positive charges feel a force in the same direction as the electric field. Negative charges feel a force in the opposite direction as the electric field. -q < 0 + q>0 But none of this affected or changed the field, which only depends on the source charge! + Relate to: ACT: "g due to two stars", lecture 29. g only depends on source mass Superposition For several point-like charges or for continuous charge distributions, we use the superposition principle: Just as the net force is the vector-sum of all the forces, the net electric field is the vector-sum of the electric fields by all the parts. ACT: Net electric field Which of the three vectors best represents the direction of the net electric field at the location of charge Q? q1 < 0 Enet A E1 q2 > 0 Q<0 B E2 C Continuous charge distributions Each small differential charge dq is like a point charge. dq (r )dV P The net E-field at point P is the vector sum (integral) of the electric field contributions from all of them: dE dq ^ ke 2 r r E dq ^ ke 2 r r enti re volume EXAMPLE: Ring Below is a ring of radius R with uniform linear charge distribution . Find the electric field along the z-axis. x P z y x dq = Rd d r R2 z2 z P y dE dq k 2 r k R2 Rd z2 x Cylindrical symmetry: only Ez matters P z dEz k dE cos R2 Rd z2 R2 zRd z z2 y k R zR z 2 z 2 3/ 2 E z , net k zR R 2 2 0 z 2 3/ 2 d k 2 R 2 2 3/ 2 From the ring to the charged disk... Disk of radius R with uniform charge surface density can be thought of as made of rings of radii r = 0 to r = R and linear charge density dr. E disk R R 0 k 2 zr z 1 2 3/ 2 r 2 dr 1 k2 z 1 R r 1 2 z 2 1/2 0 k2 z r 2 z 2 1/2 z k2 z R 2 z 2 1/2 2 1 0 z R 2 z 2 1/2 ... and to the infinite plane Take the limit R R lim 2 1 0 z R 2 z 2 1/2 2 0 Uniform electric field ! (Does not depend on distance) Example: Electron in a uniform electric field Once the electric field is known, finding the force on a given charge is trivial... Example: Describe the motion of an electron with initial velocity v ^ that enters a region with a uniform electric field E E 0 j . v 0i^ a Fnet me Fe me qeE me . qe E 0 ^ j me Constant acceleration in the j direction. Identical to projectile motion! v0 electron E F = |qe|E parabola Electric field in conductors The electric field inside a conductor in equilibrium is always zero. If E 0 F 0 a 0 motion of charges (conductor, charges can move) non equilibrium The electric field right outside a conductor in equilibrium are perpendicular to the surface of the conductor. We cannot have a force parallel to the surface (would produce motion), but perpendicular to it is OK. E=0 Electric field in insulators (or dielectrics) Charges can move only a little (polarization), so the electric field is not zero, but it is smaller than outside the insulator. Enet E ext + Epol Eext + + Enet Eext + + + Eext + + + + Epol Dielectric breakdown As Eext increases, the electric force that pulls apart the + and parts of each molecule in the insulator increases. Insulator Insulator + + + ++ Eext 0 Eext Eext = 0 stronger 0, Insulator + ++ Dielectric breakdown! When the electric force is stronger than the molecular bond, the molecule breaks apart. Conductor + ++ Eext > EMAX Dielectric strength EXAMPLE: Lightning Collisions inside clouds produce charged particles. The heavier particles are () and sit at the bottom of the cloud and the lighter particles (+) near the top. - - - - - The negative bottom attracts the positives on the ground. - - - - - - - - -- - - Factoids: When E > EMAX for air, air becomes a conductor EMAX air ~ 3x106 N/C t ~ 30 ms V ~ 20x106 V E I ~ 40,000 A P ~ 1012 W + + + + + + + + + DEMO: Lightning and fluorescent EXAMPLE: Infinite line of charge A cable of diameter D = 3 mm and length L = 200 m has a total charge Q = 4 C uniformly distributed along its length. Find the electric field at point P, located at a distance r = 2 cm from it. P r L >> r infinite cable r >> D one-dimensional charge distribution y dE P dq ke 2 d dx ke 2 x r2 dE r d x2 r2 dq = dx x x dx Linear charge density: Q L Infinite line: There is always another dq symmetrically placed. The x-components of the electric fields cancel out. dE y dx ke 2 cos 2 x r y dx r ke 2 x r2 x2 r2 ke r dx x 2 r 2 32 dE r dE d x2 r2 x x Enet dE y ke r dx x 2 r 2 32 ... 2ke r Q 2ke rL
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Iowa State - PHYS - 221
Lecture 32Electric field lines. The electric dipole.Example: The electric dipole+d-p+Q-QDefinition: Electric dipole momentpQdDirection: From to +What happens to a dipole in an external electric field?An electric dipol
Iowa State - PHYS - 221
Lecture 33Electric Flux Gauss's LawFlux in GeneralDEMO: LoopFlux: How much of something is passing through a surface.How many hairs are passing through your scalp. If you dip a tennis racquet in a river, how much water flows through it?Ma
Iowa State - PHYS - 221
Lecture 34Applications of Gauss's LawACT: Crossed planesWhich diagram corresponds to the E-field lines for these two uniformly charged infinite sheets that intersect each other as shown? +++Each sheet produces a uniform electric field
Iowa State - PHYS - 221
Lecture 35Electric Potential Energy and Electric PotentialElectric potential energyElectric forces are conservative (Coulomb's law is mathematically identical to Newton's gravitational force, which is conservative).So we can write the work done
Iowa State - PHYS - 221
Lecture 36More Example of Electric Potential. Equipotentials. Lightning rods and why you lose your radio station inside tunnels.Example: Getting the electric field from the electric potentialWe saw last time that EV5y 4z 2Example: Find t
Iowa State - PHYS - 221
Lecture 37CapacitanceCapacitorsA capacitor is a device whose purpose is to store electric energy which can be released in a controlled manner. Usually made of two conductors with charges +Q and Q.-Q+Q. separated by an insulator (dielectric)
Iowa State - PHYS - 221
Lecture 38Electric energy Capacitors with dielectricsEnergy stored in a capacitor= external work needed to charge itWork to add a charge dq to a capacitor with capacitance C and charge q:dWextdWelectricdUVdqq dq CTotal work: WextQ
Iowa State - PHYS - 221
Lecture 39Current. Resistance. Ohm's law.Electric current= charges in motion.CurrentIdQ dtUnits: A (Ampere) 1 A = 1 C/sCurrent density(current per crosssectional area)JdI dAIAfor uniform currentA = cross-sectional area(Exam
Iowa State - PHYS - 221
Iowa State - PHYS - 221
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Iowa State - PHYS - 221
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Iowa State - PHYS - 221
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Iowa State - PHYS - 221
Iowa State - PHYS - 221
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Iowa State - PHYS - 221
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Iowa State - PHYS - 221
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Iowa State - PHYS - 221
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Iowa State - PHYS - 221
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Iowa State - PHYS - 221
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Iowa State - PHYS - 221
PHYSICS 221 EXAM3
Iowa State - PHYS - 221
Mark answers in spaces 31-43 on the answer sheetPHYSICS 221 Summer 2005 EXAM 3: July 25 2005 9:50pm-10:50pmName (printed): _ ID Number: _ Section Number: __ INSTRUCTIONS:Some questions are one point, others are two points, as marked. Answer all qu
Iowa State - PHYS - 221
PHYSICS 221 Fall 2006 FINAL EXAM: December 12 2006 7:00pm-9:00pmName (printed): _ ID Number: _ Recitation Instructor: _ Section #_INSTRUCTIONS:This exam contains 28 equally weighted multiple-choice questions (24 regular questions + 4 lab question
Iowa State - PHYS - 221
PHYSICS 221 Fall 2006 FINAL EXAM: December 12 2006 7:00pm-9:00pmName (printed): _ ID Number: _ Recitation Instructor: _ Section #_INSTRUCTIONS:This exam contains 28 equally weighted multiple-choice questions (24 regular questions + 4 lab question
Iowa State - PHYS - 221
Iowa State - PHYS - 221
Iowa State - PHYS - 221
PHYSICS 221 Spring 2006 FINAL EXAM: May 2 2006 2:15pm-4:15pmName (printed): _ ID Number: _ Section Number: _ INSTRUCTIONS:Each question is of equal weight, answer all questions. All questions are multiple choice. Choose the best answer to each ques
Iowa State - PHYS - 221
Iowa State - PHYS - 221
Iowa State - PHYS - 221
PlaneAn airplane needs a minimum air speed of 100 miles per hour (Va) in order to land. The runway is at a 30 degree angle to a 25 mile per hour wind (Vb) which is blowing from the east. What is the speed relative to the ground of the airplane when
Iowa State - PHYS - 221
Iowa State - PHYS - 221
Iowa State - PHYS - 221
Iowa State - PHYS - 221
Iowa State - PHYS - 221
Iowa State - PHYS - 221
Iowa State - PHYS - 221
Iowa State - PHYS - 221
Iowa State - PHYS - 221
Iowa State - PHYS - 221
Iowa State - PHYS - 221
Iowa State - PHYS - 221
Iowa State - PHYS - 221
August28. Quiz for Tuesday, VersionA: are Two vectors givenasA:3i + 2j + k andB=2i+ 2i+ 2k. Whatisthe angle A between andB?-r-*:t)jSt\E\ cos = N*\* oN:R.r N?Rz + l-\.\5== CcrS-[A: 22,2&quot; VersionB: are Twovectors givenbyA:3i + j andB:2i-i.comp
Iowa State - PHYS - 221
August30. Quiz for Thursday, VersionA: of A car hasa speed 50 km / hr. Whenthe driver breaksashardashe canit takes4 give the is seconds cometo rest. (a) Assumingthat the acceleration constant, to process? (b) How far doesthe car moveduringthe stoppin
Iowa State - PHYS - 221
Iowa State - PHYS - 221
Quiz for Tuesduy,SeptemberI 1.A particle undergoescircular motion. It is 50 cm from the axis or rotation Version A: -Z1s-21t2. At t :2 s,what is the (a) and it moving in the x-y plane. 0(t) - 6 + 5(s-11t particle's velocity? (b) At t : 2 s, what is
Iowa State - PHYS - 221
13. September Quiz for Thursday, VersionA: Thetotal forceon a 10kg mass givenby F - (4lD i. If the mass is starts att - 0 s, at rest,at the origin,what is its (a) velocityand(b) positionat t: 4 s?/=;iF: f :q\rrrr6L--?1 r2f= J-t: ,J \
Iowa State - PHYS - 221
Iowa State - PHYS - 221
25. September Quiz for Tuesday, uniform circularmotionon a A,Zkgmass,tied to a string,undergoes version A: periodofthemotion is 4 s' If The radiusof the circle islz5r*-uod the table. horizontal is the between massandthe table'what is a coefiicientof
Iowa State - PHYS - 221
27. Quiz for Thursday,SeptemberHow fast would a 7A kg person have to climb stairs to conzumethe same Version A: amount of power as a 1000W light bulb? Give answerin km / h.= p=+{pr.o = rn?\&quot;1 =r ., ' r =(c&quot;tr\(tr ' \&quot;)t\t) TEKw d\t 6583- = \1.,0
Iowa State - PHYS - 221
Iowa State - PHYS - 221
Iowa State - PHYS - 221
October16. Quiz for Tuesday, aboutana:ris VersionA: A solidsphere with massl0 kg andradius15cm is rotated its thattouches edge. (a) Whatis the sphere's moment inertiaforthis rotation?(b) Ifa of pointinginto the page, forceof 15N is applied whatis the
Iowa State - PHYS - 221
Iowa State - PHYS - 221
Iowa State - PHYS - 221
30. October Quiz for Tuesday, A sphere VersionA: with a radiusof 20.0 cm anda massof 2.00 kg is hungsothat it point on its edge. What is the periodof the sphere's motionif it osc,iltalgg rotatesaboutawitha small amplitude? t- N FoPU&quot;t\CALi\EtJs