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Electric Field Point charge: Dipole: for r>>s : at +q -q s x y z at Dipole moment: p = qs Uniformly charged sphere: for r>R (outside) for r

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Presentation on theme: "Electric Field Point charge: Dipole: for r>>s : at +q -q s x y z at Dipole moment: p = qs Uniformly charged sphere: for r>R (outside) for r

1 Electric Field Point charge: Dipole: for r>>s : at +q -q s x y z at Dipole moment: p = qs Uniformly charged sphere: for r>R (outside) for r

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3 What is the magnitude of the net electric field at location X, due to these two charges? Assume d >> s Clicker Question 1 +2e-e-e s d X Choice A B C What is the approximate magnitude? Choice A B C

4 Clicker Question 2 + A C d d - d B

5 What is the direction of the electric field at location X, due to the dipole? Clicker Question 3 A C B E D - + X

6 Clicker Question

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9 Choice of System Multiparticle 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 field the charge that is affected by that field

10 Convenience: know E at some location – know the electric force on any charge: Example: if E > 3  10 6 N/C air becomes a conductor Retardation Nothing can move faster than light c c = 300,000 km/s = 30 cm/ns Electric properties of matter– independent of how this field was produced. Coulomb’s law is not completely correct – it does not contain time t nor speed of light c. v<

11 Chapter 15 Matter and Electric Fields

12 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 electron net charge = (+e) + (-e)=0 Sodium atom: 11 protons, 11 electrons Sodium atom (Na) can lose an electron: Sodium ion (Na + ): (+11e) + (-10e) = +e Ordinary matter is electrically neutral. However, can be charged by adding/removing charged particles Net Charge

13 The net charge of a system and its surroundings cannot change If one object gets charged positively, there must be an object which gets charged negatively. Conservation of Charge The net electric charge is conserved in any physical process. Charge can be transferred from one object to another.

14 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 charge the magnitude of E decreases with distance the direction of E points directly away or to the charge force has the same properties as E Observing Electric Interactions

15 1.Interaction of two U tapes Repel, attract or no interaction? Is it an electric interaction? direction distance dependence dependence on the amount of charge repel: like charges     Two U tapes are charged and charges are of the same sign Experiments with Tape Does the tape have nonzero net charge?

16 How would we make two tapes with opposite charges? 2.Interaction of U and L tapes Repel, attract or no interaction? Is it electric interaction? direction distance dependence dependence on the amount of charge attract: opposite charges     U (upper) and L (lower) tapes are oppositely charged. Unlike Charges

17 Conclusions of experiments with U and L tapes: There are two kinds of charges (+, -) Like charges repel, unlike charges attract The 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. Experiments with Tape

18 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? Breaking large molecules, transfer ions Transfer electrons  Why positive or negative? Don’t know Determining Sign of the Charge

19 Interaction of Charges and Neutral Matter Interaction of U and L tapes with other objects: Plastic pen Paper Hand Metal Net charge is zero! Why does it interact?

20 m (1 Å) Nucleus, ~ m Charge 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. Hydrogen The Structure of an Atom

21 + 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. +- Polarization of Atoms

22 it is not a permanent dipole E an induced dipole is created when a neutral object is polarized by an applied electric field An applied electric field creates induced dipoles! Induced Dipole

23 Polarization Amount of polarization p in most materials is proportional to the magnitude of the applied electric field: In an induced dipole, is the distance between the charges fixed? The distance is proportional to the strength of the applied field. E E

24 Shift is five orders of magnitude smaller than the atom itself! Example But can still cause lightning (air becomes conductor)!

25 1. Charge q 1 creates field E 1 at the location of the atom A Neutral Atom and a Point Charge

26 2. Field E 1 polarizes the atom creating a dipole 1) A Neutral Atom and a Point Charge

27 3. Dipole creates field E 2 at the location of q 1 1) 2) A Neutral Atom and a Point Charge

28 4. Induced dipole exerts force F 1 on the charge: 1) 2) 3) A Neutral Atom and a Point Charge

29 5. The charge q 1 exerts force F 2 on the dipole (reciprocity): 1) 2) 3) 4) A Neutral Atom and a Point Charge

30 1) 2) 3) 4) 5) Neutral atoms are attracted by charges! Interaction strength ~ 1/r 5 A Neutral Atom and a Point Charge

31 Atom A is easier to polarize than atom B. Which atom would experience a greater attraction to a point charge a distance r away? A B FAFA FBFB Exercise

32 Interaction of Charged Tapes and Neutral Matter

33 Repulsion: FRFR Attraction: FAFA Total: q1q1 q2q2 Interaction of like-charged Objects ConductorPlastic

34 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!  Attraction: can happen for like-charged objects! Repulsion: can happen only for like-charged objects! Determining the Charge of an Object

35 FF The field appears to be weaker in presence of intervening (polarizable) object. Both tapes are attracted to paper Superposition principle: the presence of matter does not affect the electric field produced by a charged object. Intervening matter does not “block” the E field The resulting field is a superposition of two fields: Field of the other charge plus the field of induced dipoles. Electric Field Through Intervening Matter

36 Interaction of Charged Tapes and Neutral Matter

37 Electrostatic Precipitator Energy, Environment and Climate, Richard Wolfson


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