3 Clicker Question 1 +2e -e s d What is the magnitude of the net electric field at location X, due to these two charges? Assume d >> s+2e-esdXWhat is the approximatemagnitude?Choice𝑬 𝒏𝒆𝒕A1 4𝜋 𝜀 0 𝑒𝑠 𝑑 3B1 4𝜋 𝜀 0 2𝑒𝑠 𝑑 3C𝑛𝑜𝑛𝑒𝑜𝑓 𝑡ℎ𝑒𝑠𝑒Choice𝑬 𝒏𝒆𝒕A1 4𝜋 𝜀 0 𝑒 𝑑 2B1 4𝜋 𝜀 0 2𝑒𝑠 𝑑 3C1 4𝜋 𝜀 𝑒𝑠 𝑑 3Answer: C, A
4 Clicker Question 2Locations A, B, and C are equidistant from the center of the dipole (charges +q and –q are separated by s). At which location(s) is the magnitude of the electric field approximately 𝟏 𝟒𝝅 𝜺 𝟎 𝒒𝒔 𝒅 𝟑 ?at location Aat location Bat location Cat locations A, Cat locations A, B, Cd-+AddAnswer: ABC
5 Clicker Question 3What is the direction of the electric field at location X, due to the dipole?-+CBDXAnswer: BEA
9 Choice of SystemMultiparticle systems: Split into objects to include into system and objects to be considered as external.To use field concept instead of Coulomb’s law we split the Universe into two parts:the charges that are the sources of the fieldthe charge that is affected by that field
10 A Fundamental Rationale Convenience: know E at some location – know the electric force on any charge:Electric properties of matter– independent of how this field was produced.Example: if E > 3106 N/C air becomes a conductorRetardationNothing can move faster than light cc = 300,000 km/s = 30 cm/nsCoulomb’s law is not completely correct – it does not contain time t nor speed of light c.Example: Suppose I am negatively charged sphere, move to one side ask student in back row to show the direction of E due to this charge.Then move to the other side at ~speed of light and ask student what will happen to E. It is ~5 meters, so it takes 15 ns for E to change direction after I moved!More drastic example – pretend that I hold electron and positron (dipole), ask student to show E. Collapse (annihilate) charges and count time.Conclusion: E can exist independently of charges!!!Does not contain v – works only when speed is << cv<<c !!!
12 Net Charge Matter is made out of atoms. Atom contains charged particles: electrons (-e), protons (+e)Neutral atom: number of electrons and protons is equal:Example: Hydrogen atom: 1 proton, 1 electronnet charge = (+e) + (-e)=0Sodium atom: 11 protons, 11 electronsSodium atom (Na) can lose an electron:Sodium ion (Na+): (+11e) + (-10e) = +eIf we remove all electrons from human body charge will be 70kg/1.7e-27kg*1.6e-19C=6.6e9 C, 6 billion Coulomb.If you and I are separated by the Earth-moon distance of 4 x 10^8 m, Force = 9e9*(6.6e9)^2/16e16 = 2.4e12 NOrdinary matter is electrically neutral.However, can be charged by adding/removing charged particles
13 Conservation of Charge The net charge of a system andits surroundings cannot changeIf one object gets charged positively, there must be an object which gets charged negatively.The net electric charge is conserved in any physical process.Charge can be transferred from one object to another.Pair-Production: 𝛾 → 𝑒 + + 𝑒 −Example: when you comb your hair the comb gets charged and so does your hair, the magnitude is equal, sign is different.
14 Observing Electric Interactions How can we decide if a piece of invisible tape is electrically charged?Charge creates E field; detected by another charged object:the magnitude of E is proportional to amount of chargethe magnitude of E decreases with distancethe direction of E points directly away or to the chargeforce has the same properties as E
15 Experiments with Tape Does the tape have nonzero net charge? Interaction of two U tapesRepel, attract or no interaction?repel: like chargesIs it an electric interaction?directiondistance dependencedependence on the amount of chargeTwo U tapes are charged and charges are of the same sign
16 Unlike Charges How would we make two tapes with opposite charges? 2. Interaction of U and L tapesRepel, attract or no interaction?attract: opposite chargesIs it electric interaction?directiondistance dependencedependence on the amount of chargeU-tape is attracted to plastic rubbed through your hair (negative). L-tape is repelled.U – positive, L-negative.i.e. When you tear tape off surface it leave electrons.U (upper) and L (lower) tapes are oppositely charged.
17 Experiments with Tape Conclusions of experiments with U and L tapes: There are two kinds of charges (+, -)Like charges repel, unlike charges attractThe electric force:acts along a line between the charges,decreases rapidly as the distance between the charges increases,is proportional to the amounts of both charges.Our observations of U and L tapes seem to be consistent with a description of the electric interactions between charged objects. We conclude that U and L tapes are electrically charged, and have unlike charges.
18 Determining Sign of the Charge How would we determine the sign of the charge?Comb (or plastic pen) gets negatively charged when rubbed through hair, fur or wool; glass rod becomes positively charged.Why get charged?Why? Ask students if anyone knows – that’s fine, no one really knows details of this process.Go by book.U-tape is attracted to plastic rubbed through your hair (negative). L-tape is repelled.U – positive, L-negative.i.e. When you tear tape off surface it leave electrons.Breaking large molecules, transfer ionsTransfer electronsWhy positive or negative?Don’t know
19 Interaction of Charges and Neutral Matter Interaction of U and L tapes with other objects:Plastic penPaperHandMetalNet charge is zero! Why does it interact?
20 The Structure of an Atom Hydrogen10-10 m (1 Å)Nucleus, ~10-15 mCharge of electron cloud equals that of nucleus neutral atom.If the electron cloud is centered on the nucleus electric field produced by electrons exactly cancels the field produced by nucleus.
21 Polarization of Atoms E + - + Force due to E created by positive charge shifts electron cloud and nucleus in opposite directions: electric dipole.An atom is said to be polarized when its electron cloud has been shifted by the influence of an external charge so that the electron cloud is not centered on the nucleus.
22 Induced Dipole An applied electric field creates induced dipoles! E it is not a permanent dipolean induced dipole is created when a neutral object is polarized by an applied electric field
23 PolarizationAmount of polarization p in most materials is proportional to the magnitude of the applied electric field:𝛼 - “polarizability” of a materialIn an induced dipole, is the distance between the charges fixed?The distance is proportional to the strength of the applied field.+−+E− +E
24 Example A typical atomic polarizability is 𝛼=10-40 C•m/(N/C). If q=e (proton charge), what is the charge separation by applying a field E=3x106 N/C?The value chosen for E here is that which causes air to become conducting. Turning the above argument around, we see that a displacement of only 2x10^-15 m causes an E field capable of ionizing air.Shift is five orders of magnitude smaller than the atom itself!But can still cause lightning (air becomes conductor)!
25 A Neutral Atom and a Point Charge 1. Charge q1 creates field E1 at the location of the atom
26 A Neutral Atom and a Point Charge 1)2. Field E1 polarizes the atom creating a dipole
27 A Neutral Atom and a Point Charge 1)2)3. Dipole creates field E2 at the location of q1
28 A Neutral Atom and a Point Charge 1)3)2)4. Induced dipole exerts force F1 on the charge:1/r^5 because induced p proportional to 1/r^2 and it produces a field at q1 proportional to p/r^3.
29 A Neutral Atom and a Point Charge 1)3)2)4)5. The charge q1 exerts force F2 on the dipole (reciprocity):
30 A Neutral Atom and a Point Charge 1)2)3)4)5)Neutral atoms are attracted by charges!Interaction strength ~ 1/r5
31 ExerciseAtom A is easier to polarize than atom B. Which atom would experience a greater attraction to a point charge a distance r away?+-FAFBA+-B
32 Interaction of Charged Tapes and Neutral Matter
33 Interaction of like-charged Objects q1q2FRFAConductorPlasticRepulsion:Attraction:Left object is a conductor, right object is nonconductor, polarizable.Total:
34 Determining the Charge of an Object Suppose tape is negatively charged, and you rub a wooden pencil on a wool sweater and bring it near the tape.-----If tape swings toward the pencil, does it show that the pencil had been charged positively?NOT NECESSARILY!Suppose tape is negatively charged, and you rub a wooden pencil on a wool sweater and bring it near the tape:Attraction: can happen for like-charged objects!Repulsion: can happen only for like-charged objects!
35 Electric Field Through Intervening Matter The field appears to be weaker in presence of intervening (polarizable) object. Both tapes are attracted to paperSuperposition principle: the presence of matter does not affect the electric field produced by a charged object.If instead, we put a conductor between the two charged objects, the field would be enhanced. See WebAssign homework.Intervening matter does not “block” the E fieldThe resulting field is a superposition of two fields:Field of the other charge plus the field of induced dipoles.
36 Interaction of Charged Tapes and Neutral Matter
37 Electrostatic Precipitator Energy, Environment andClimate, Richard Wolfson