Electic Field Point chage: E " ˆ Unifomly chaged sphee: E sphee E sphee " Q ˆ fo >R (outside) fo <R (inside) - Dipole: fo >>s : E " s 3,, at <,,> z y s + x Dipole moment: p s E E s "#,, 3 s "#,, 3 at <,,> at <,,>
Choice of System Multipaticle systems: Split into objects to include into system and objects to be consideed as extenal. To use field concept instead of Coulomb s law we split the Univese into two pats: the chages that ae the souces of the field the chage that is affected by that field Example: Oscilloscope Chages on metal plates ae the souces of an unifom E field
A Fundamental Rationale Convenience: know E at some location know the electic foce on any chage: F E Can descibe the electic popeties of matte in tems of electic field independent of how this field was poduced. Example: if E > 3x 6 N/C ai becomes conducto Retadation Nothing can move faste than light c c 3, km/s 3 cm/ns Coulomb s law is not completely coect it does not contain time t no speed of light c. F " ˆ E " ˆ v<<c
Chapte 5 Matte and Electic Fields
Net Chage Matte is made out of atoms. Atom contains chaged paticles: electons (-e), potons (+e) Neutal atom: numbe of electons and potons is eual: Example: Hydogen atom: poton, electon net chage (+e) + (-e) Sodium atom: potons, electons Sodium atom (Na) can lose an electon: Sodium ion (Na + ): (+e) + (-e) +e Odinay matte is electically neutal. Howeve, can be chaged by adding/emoving chaged paticles
Consevation of Chage The net chage of a system and its suoundings cannot change If one object gets chaged positively, thee must be an object which gets chaged negatively. The net electic chage is conseved in any physical pocess. Chage can be tansfeed fom one object to anothe. Annihilation : e + + e " + "
Obseving Electic Inteactions How can we decide if a piece of invisible tape is electically chaged? Chage ceates E field; detected by anothe chaged object: the magnitude of E is popotional to amount of chage the magnitude of E deceases with distance the diection of E points diectly away o to the chage F E foce has the same popeties as E
Expeiments with Tape Does the tape have nonzeo net chage?. Inteaction of two U tapes Repel, attact o no inteaction? Is it an electic inteaction? diection distance dependence dependence on the amount of chage epel: like chages Two U tapes ae chaged and chages ae of the same sign
Unlike Chages How would we make two tapes with opposite chages?. Inteaction of U and L tapes Repel, attact o no inteaction? Is it electic inteaction? diection distance dependence dependence on the amount of chage attact: opposite chages U (uppe) and L (lowe) tapes ae oppositely chaged.
Expeiments with Tape Conclusions of expeiments with U and L tapes: Thee ae two kinds of chages (+, -) Like chages epel, unlike chages attact The electic foce: acts along a line between the chages, deceases apidly as the distance between the chages inceases, is popotional to the amounts of both chages. Ou obsevations of U and L tapes seem to be consistent with a desciption of the electic inteactions between chaged objects. We conclude that U and L tapes ae electically chaged, and have unlike chages.
Detemining Sign of the Chage How would we detemine the sign of the chage? Comb (o plastic pen) gets negatively chaged when ubbed though hai, fu o wool; glass od becomes positively chaged. Why get chaged? Beaking lage molecules, tansfe ions Tansfe electons Why positive o negative? Don t know
Inteaction of Chages and Neutal Matte Inteaction of U and L tapes with othe objects: Plastic pen Pape Hand Metal Net chage is zeo Why does it inteact?
The Stuctue of an Atom Hydogen - m ( Å) Nucleus, ~ -5 m Chage of electon cloud euals that of nucleus neutal atom. If the electon cloud is centeed on the nucleus electic field poduced by electons exactly cancels the field poduced by nucleus.
Polaization of Atoms + E - + Foce due to E ceated by positive chage shifts electon cloud and nucleus in opposite diections: electic dipole. An atom is said to be polaized when its electon cloud has been shifted by the influence of an extenal chage so that the electon cloud is not centeed on the nucleus.
Induced Dipole An applied electic field ceates induced dipoles E it is not a pemanent dipole an induced dipole is ceated when a neutal object is polaized by an applied electic field
Polaization Amount of polaization p in most mateials is popotional to the magnitude of the applied electic field: p E α - polaizability of a mateial In an induced dipole, is the distance between the chages fixed? The distance is popotional to the stength of the applied field.
A typical atomic polaizability is α - C m/(n/c). If e (poton chage), what is the chage sepaation by applying a field E3 6 N/C? p E " # 3 # 6 (C $ m) 3 # "3 C $ m p s Example s p 3 "3.6 "9 m # "5 m Shift is five odes of magnitude smalle than the atom itself
A Neutal Atom and a Point Chage. Chage ceates field E at the location of the atom E " ˆ
A Neutal Atom and a Point Chage ) E " ˆ. Field E polaizes the atom ceating a dipole p E "# ˆ
A Neutal Atom and a Point Chage ) ) E p " "# ˆ ˆ 3. Dipole ceates field E at the location of E p " # E 3 " 3 $ & % " ) ( # 5 ˆ
. Induced dipole exets foce F on the chage: E ˆ " E F ˆ 5 "# $$ % & ( ) p ˆ "# E ˆ 5 "# $$ % & ( ) ) ) 3) A Neutal Atom and a Point Chage
5. The chage exets foce F on the dipole (ecipocity): E ˆ " F F ˆ 5 "# $$ % & ( ) * * p ˆ "# E ˆ 5 "# $$ % & ( ) F ˆ 5 "# $$ % & ( ) ) ) 3) ) A Neutal Atom and a Point Chage
E ˆ " p ˆ "# E ˆ 5 "# $$ % & ( ) F ˆ 5 "# $$ % & ( ) ) ) 3) ) F ˆ 5 "# $$ % & ( ) * 5) Neutal atoms ae attacted by chages Inteaction stength ~ / 5 A Neutal Atom and a Point Chage
Execise Atom A is easie to polaize than atom B. Which atom would expeience a geate attaction to a point chage a distance away? A - + F A B - + F B ) F "# $ & ( % 5 ~
Inteaction of Chaged Tapes and Neutal Matte
Inteaction of like-chaged Objects F R Conducto F A Plastic Repulsion: F R " ˆ Attaction: Total: F A F ) & * N ˆ 5 ( "# $$ % &, ). N ˆ 5 # $ - * $ / % + / ( "
Detemining the Chage of an Object Suppose tape is negatively chaged, and you ub a wooden pencil on a wool sweate and bing it nea the tape. - - - - If tape swings towad the pencil, does it show that the pencil had been chaged positively? NOT NECESSARILY Attaction: can happen fo like-chaged objects Repulsion: can happen only fo like-chaged objects
Electic Field Though Intevening Matte F F The field appeas to be weake in pesence of intevening (polaizable) object. Supeposition pinciple: the pesence of matte does not affect the electic field poduced by a chaged object. Intevening matte does not block the E field The esulting field is a supeposition of two fields: Field of the othe chage plus the field of induced dipoles.