l02 electric forces

8/8/2019 L02 Electric Forces

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Electric Field LinesElectric Field LinesDescribe the d irectio n of the electric fiel d at a n y poi n tDescribe the d irectio n of the electric fiel d at a n y poi n tThe d e n sity of fiel d lin es is proportio n al to the ma g n it ud e of The d e n sity of fiel d lin es is proportio n al to the ma g n it ud e of the electric fiel d.the electric fiel d.

The d irectio n s of arrows i nd icate the d irectio n of the force o n aThe d irectio n s of arrows i nd icate the d irectio n of the force o n apositive test char g e .positive test char g e .R ulesR ules ::

lin es be g in o n + char g e a nd e nd o n lin es be g in o n + char g e a nd e nd o n char g e . char g e .d e n sity of li n es ( nu mber of li n es per area) approachi n g ord e n sity of li n es ( nu mber of li n es per area) approachi n g orleavi n g a char g e is proportio n al to the ma g n it ud e of theleavi n g a char g e is proportio n al to the ma g n it ud e of thechar g e .char g e .

electric fiel d lin es may n ever cross (electric fiel d lin es may n ever cross ( if they crossed, theif they crossed, theelectric field would not have a uni q ue direction at that electric field would not have a uni q ue direction at that position position ) .) .


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Electric Field LinesElectric Field Lines


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Electric Field LinesElectric Field Lines

An imatio n : Char g es a nd F iel d s


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Electric Field M odelsElectric Field M odelsElectric fiel d g e n erate d by aElectric fiel d g e n erate d by a si n g le poi n t char g esi n g le poi n t char g e::

Electric fiel d g e n erate d by aElectric fiel d g e n erate d by a d iscrete d istrib u tio nd iscrete d istrib u tio n of char g es:of char g es:

Electric fiel d g e n erate d by aElectric fiel d g e n erate d by a co n ti nu o u s d istrib u tio nco n ti nu o u s d istrib u tio n : i n te g ratio n : i n te g ratio n m u st be u se d (represe n t a macroscopic object as a collectio n of m u st be u se d (represe n t a macroscopic object as a collectio n of small char g es, a nd take a limit where char g es become poi n tsmall char g es, a nd take a limit where char g es become poi n t --like) . The i n te g ratio n simplifies whe n the char g e is d istrib u te d like) . The i n te g ratio n simplifies whe n the char g e is d istrib u te d un iformly thro u g ho u t a symmetric object (e . g . lo n g wire,un iformly thro u g ho u t a symmetric object (e . g . lo n g wire,pla n e, sphere, d isk, etc)pla n e, sphere, d isk, etc)

r r

qk E !

T

!!

!! N

ii

i

i N

iinet r

r

qk E E

12

1

TT

L ink:L ink: Field lines for variousField lines for variouscharge configurationscharge configurations


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Electric DipoleElectric DipoleElectric di poleElectric di pole co n sists of two opposite char g es (co n sists of two opposite char g es ( + q+ q a nd a nd qq),),

separate d by a small d ista n ceseparate d by a small d ista n ce s s. Net char g e is zero, b u t n et fiel d is. Net char g e is zero, b u t n et fiel d isn ot . n ot . D i pole moment D i pole moment :: positive)tonegativefrom;( sq p !T

axis)thetonormal(

axis)sdipole'thealong(

2

3

3||

r p

k E

r

pk E

T

T

T

T

B

An imatio n : I d e n tify the char g es


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Example: multiple chargesExample: multiple chargesCalc u late the electric fiel d at poi n t O (see fi g u res below)Calc u late the electric fiel d at poi n t O (see fi g u res below)


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Charged Particle in a FieldCharged Particle in a FieldCo n si d er a particle of massCo n si d er a particle of mass mm a nd char g ea nd char g e qq . Its. Its chargecharge- -toto--massmass

ratioratio :: q/m. . F orce o n the particle from the fiel d :F orce o n the particle from the fiel d :Acceleratio n :Acceleratio n :Un iform fiel d : fiel d stre n g th E is co n sta n t, so is theUn iform fiel d : fiel d stre n g th E is co n sta n t, so is theacceleratio n. Trajectory: parabola (same type as for projectileacceleratio n. Trajectory: parabola (same type as for projectilemotio n ) . motio n ) .

E q F

TT

!

E mqm F a

TTT

)/(/ !!


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Example: electron between the platesExample: electron between the platesAn electro n is la un che d at a 4 5An electro n is la un che d at a 4 5 00 a n g le a nd a spee d of a n g le a nd a spee d of 5*

105*

1066

m/s from the positive plate of the parallelm/s from the positive plate of the parallel -- plateplatecapacitor, a nd la nd s 4cm away . Ne g lect the g ravity .capacitor, a nd la nd s 4cm away . Ne g lect the g ravity .F ind : i) electric fiel d in si d e the capacitor; ii) mi n im u m spaci n g F ind : i) electric fiel d in si d e the capacitor; ii) mi n im u m spaci n g betwee n the plates .betwee n the plates .


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l02 electric forces

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