Electric Field y x z Point charge: Uniformly charged sphere: Dipole: for r>R (outside) for r<R (inside) Dipole: for r>>s : at <r,0,0> at <0,r,0> +q -q s x y z at <0,0,r> Dipole moment: p = qs

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 -e s d X What is the approximate magnitude? Choice 𝑬 𝒏𝒆𝒕 A 1 4𝜋 𝜀 0 𝑒𝑠 𝑑 3 B 1 4𝜋 𝜀 0 2𝑒𝑠 𝑑 3 C 𝑛𝑜𝑛𝑒 𝑜𝑓 𝑡ℎ𝑒𝑠𝑒 Choice 𝑬 𝒏𝒆𝒕 A 1 4𝜋 𝜀 0 𝑒 𝑑 2 B 1 4𝜋 𝜀 0 2𝑒𝑠 𝑑 3 C 1 4𝜋 𝜀 0 1.5𝑒𝑠 𝑑 3 Answer: C, A

Clicker Question 2 Locations 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 A at location B at location C at locations A, C at locations A, B, C d - + A d d Answer: A B C

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

Clicker Question C

Clicker Question

Clicker Question C

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

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 > 3106 N/C air becomes a conductor Retardation Nothing can move faster than light c c = 300,000 km/s = 30 cm/ns Coulomb’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 << c v<<c !!!

Chapter 15 Matter and Electric Fields

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 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 If 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 N Ordinary matter is electrically neutral. However, can be charged by adding/removing charged particles

Conservation of Charge 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. 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.

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 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

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

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

Experiments with Tape 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.

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 ions Transfer electrons Why positive or negative? Don’t know

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?

The Structure of an Atom Hydrogen 10-10 m (1 Å) Nucleus, ~10-15 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.

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.

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

Polarization Amount of polarization p in most materials is proportional to the magnitude of the applied electric field: 𝛼 - “polarizability” of a material In an induced dipole, is the distance between the charges fixed? The distance is proportional to the strength of the applied field. + −+ E − + E

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)!

A Neutral Atom and a Point Charge 1. Charge q1 creates field E1 at the location of the atom

A Neutral Atom and a Point Charge 1) 2. Field E1 polarizes the atom creating a dipole

A Neutral Atom and a Point Charge 1) 2) 3. Dipole creates field E2 at the location of q1

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.

A Neutral Atom and a Point Charge 1) 3) 2) 4) 5. The charge q1 exerts force F2 on the dipole (reciprocity):

A Neutral Atom and a Point Charge 1) 2) 3) 4) 5) Neutral atoms are attracted by charges! Interaction strength ~ 1/r5

Exercise Atom A is easier to polarize than atom B. Which atom would experience a greater attraction to a point charge a distance r away? + - FA FB A + - B

Interaction of Charged Tapes and Neutral Matter

Interaction of like-charged Objects q1 q2 FR FA Conductor Plastic Repulsion: Attraction: Left object is a conductor, right object is nonconductor, polarizable. Total:

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!

Electric Field Through Intervening Matter 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. 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 field The resulting field is a superposition of two fields: Field of the other charge plus the field of induced dipoles.

Interaction of Charged Tapes and Neutral Matter

Electrostatic Precipitator Energy, Environment and Climate, Richard Wolfson