This Week. Last Week. Another way of thinking about nature. Why invent the concept of field? Looking at interactions a new way Electric Field

Size: px

Start display at page:

Download "This Week. Last Week. Another way of thinking about nature. Why invent the concept of field? Looking at interactions a new way Electric Field"

Emery Grant
7 years ago
Views:

1 ing the effect of seveal electic chages ing the effect of man electic chages Cause b etene objects Qui Last Week! $ i This Week Looking at inteactions a new wa lectic iel The elationship of lectic oce & lectic iel Chapte 6 sections, 7 0 Wh invent the concept of fiel? We know that a chage object eets a foce on anothe chage object _ It is stange that: cause b = k cause b = k. The same chage object () has a iffeent effect on chage object () epening on the chage of.. Chage object () can eet a foce on chage object () even though the ae sepaate b a istance. How oes etemine that is neab? nothe wa of thinking about natue n chage object () changes the space aoun it. This point is change b object. So is eve othe point is space. When anothe chage object () is at that point in space it is affecte b the space. The space causes a foce on. Since the space causes a vecto effect (a foce) Descibe the effect of chage object on eve point in space as a vecto. If the space is futhe awa fom the chage object, the effect on the space is smalle. If the chage of the object is lage, the effect on space (the fiel) is lage = k If object has a negative chage, it has a iffeent effect on space. The electic fiel is in the opposite iection. If anothe chage object () is in the space affecte, inteacts with the space whee it is locate. The foce epeiences is cause b the fiel (cause b ) at that point. ve point in space the same istance fom the chage object is affecte the same wa epesente b smalle vectos at each point in space. This vecto popet of space is calle the electic fiel In this moel of natue, the effect of a chage object oes not epen on an othe object. The inteaction of the chage object () with the space at its location epens on the chage of object (). = If the chage of object is, the foce is in the same iection as the fiel. If its chage is, the foce is in the opposite iection as the fiel.

2 In this moel of natue, the foce on a chage object oes not epen on an inteaction at a istance. It inteacts onl with the space o object it touches. The concept of fiels is useful because It sepaates the inteaction into two inepenent pieces.. You etemine the fiel onl fom the popeties of the object causing the fiel. You etemine the foce on an object onl fom the popeties of that object an the fiel whee that object is. If fiels eist, then the shoul have obsevable conseuences plain ol phenomena that wee msteious. Peict new phenomena that can be foun. o eample Ol phenomena Whee is the eneg stoe in a capacito? It is in the electic fiel in the space between the two conuctos. Space can have eneg because it has popeties (fiels). New phenomena If space has eneg, then that eneg can be tansmitte b the fiels. neg tansfee though space. (cell phone signals) Using oces compae with 8 = = 8 cause b = k = k 8 cause b = k = k 8 gees with Newton s Law Seems to contaict intuition Consie this situation using iels The fiel at is cause b 8 = k 8 = k To get the foce on, multipl b = = k 8 The fiel at is cause b 8 = k = k > Much moe intuitive, the effect of is geate than the effect of To get the foce on, multipl b = = 8k = 6 Calculating the lectic iel The electic fiel is a vecto cause b chage objects. The electic fiel at an point in space is the vecto sum of the electic fiels fom all of the chage objects causing that fiel at that point in space. Simple but impotant eample lectic ipole Constucting the electic fiel vectos at each of the points gives L. The fiel at the following point is most closel in which iection? = = = = Calle a fiel map. = 7 8

3 . The foce on an electon at the same point is most closel in which iection? 8 is the closest iection. The foce on a soium ion () at the same point is most closel in which iection? Yestea Intouce the concept of fiel The electic fiel is a popet of space cause b an electic chage is a vecto at eve point in space Diection wa fom chage Towa chage Magnitue = k If anothe chage object () occupies the place with an electic fiel cause b (). That object () epeiences a foce Diection of foce In iection of fiel if has a chage In opposite iection of fiel if has a chage You team nees to moif an electon micoscope to get cleae images of bain tissue. One suggestion is to eplace the plate that acceleates the electons with a conucting ing. lectons woul oiginate fom a hot filament at the cente of the ing. The negativel chage ing woul then cause them to acceleate. s an initial test of the esign, ou have been aske to calculate the electic fiel along the ais though the cente of the ing as a function of the istance fom its cente as well as its popeties. 9 Magnitue of foce = 0 Two point chages ae locate on lectic fiel is a vecto. Continue fining electic fiel fom a Q opposite sies of an unchage ing as Know: = k chage istibution shown. What is the Q magnitue of the Q electic fiel a istance along the ais cause b the Question: two point chages? What is the electic fiel at the point a = k Question: istance along the ais of the ing which has a aius an a chage Q? () = 0 What is the electic fiel at the point a ing vectos means aing components ppoach: () = k istance along the ais of the ing = = 0 which has a aius an a chage Q? Know the electic fiel fo a point chage = k 9 () = k = = 0 ppoach: = Know the electic fiel fo a point up the electic fiels fom all of the () = k = cos = cos chage point chages aoun the ing. = k integate () = k cos θ = k 9 efoe integation eview how to cos θ = up the electic fiels fom all of (6) the point chages aoun the ing. calculate the electic fiel fom just two = k chages = k () integate

4 Q Nee to a up all the electic fiel fom all of the small chages that make up the ing. Use components = cos = sin Yestea egan to calculate the electic fiel cause b a chage ing along the ais of the ing. Q Ientif a small piece of chage on the ing. Call it This small chage causes a small electic fiel Call it = k The electic fiel is the sum of the small electic fiels cause b all of the small chages on the ing Cannot a the small electic fiels to get the total because the electic fiel is a vecto. Must a components to fin,, = = k cos θ ll of the small chages aoun the ing give an electic fiel component in the same iection. Q Just a them up. = $ ing ll of the small chages aoun the ing give an electic fiel component in iffeent iections. Some a an some subtact o eve small chage on the uppe half of the ing thee is one on the lowe half. The components cancel. = 0 The same wa The components cancel = 0 om this component analsis = up the components cause b all of the small chages that make up the total chage of the ing. = $ ing = $ k cos θ ing Take out of the integal all of the uantities that on t epen which small chage ou choose. = = k cos θ $ ing The istance of eve small chage to the point is the same. The angle of eve small chage to the ais is the same. ing up all of the small chages aoun the ing $ = Q ing = k cos θ Q Nee to know an cos Q = k Q Q = k = Q = k cos θ = = ( ) / Q = k 9 Check units Since electic fiel has units [/Q] an foce has units [kq / ] electic fiel has units [kq/ ] The answe has coect units Note that this is NOT the same as the electic fiel fom a point chage valuate: = k Q 9 If the point is ve fa fom the ing, >>, it shoul look like a point chage. = k Q = k Q 9 = k Q 9 9 Yes this is the fiel fom a point chage. 6

5 What is the electic fiel nea a lage flat plate with unifom chage Q? Q The electic fiel is the sum of the electic fiels cause b each iniviual chage on the plate. The electic fiel cause b a flat suface oes NOT epen on the istance fom that suface. Q = k Q flat plate is the suface of a eall big sphee s long as ou sta awa fom the ens, The electic fiel cause the electic fiel is the same evewhee at b a sphee is the same as the same istance fom the plate. fo a point chage at its cente = k Q The electic fiel at a istance fom a = plate is the same as at a istance. Q Q = k >> = k Q The electic fiel oes not epen on the istance fom the suface 7 Now put oppositel chage flat plates togethe One with unifom chage Q One with unifom chage Q Q lectic fiel is the same evewhee Q lectic fiel is the same evewhee ing the plates close togethe Q Q lectic fiel outsie the plates cancels No fiel outsie the plates lectic fiel between the plates as Unifom fiel between the plates fiel fom one plate Q Q 8 What happens to a ipole in a unifom electic fiel? Sum of the foces on the ipole is 0. The electic fiel causes a toue on the ipole. When ipole ais aligne with fiel No toue The ipole oscillates back an foth aoun the electic fiel iection Dipole goes past fiel iection Toue eveses eviewing toue pivot t = cos in this case = cos To use intuition, the iection of the toue is the wa an object will spin. clockwise t = is the component of pepenicula to If something spins clockwise it oes not move in a single iection. Nee to escibe toue as having a single iection along a cooinate ais. Thee is no single iection in the plane of the sceen that can escibe the toue. 9 Since toue iection cannot be in the plane of the sceen it must be pepenicula to the plane of the sceen Which iection? In o out? To be consistent, efine the ight han ule Cul finges of ou ight han in the iection that the object woul spin. You thumb points in the iection of the toue Toue is into the sceen Toue is out of the sceen If ou on t want to use intuition, use mathematics fo the iection. Vecto cosspouct τ = τ Cul ou finges fom to though the smallest angle, ou thumb points in the iection of the toue Toue magnitue o this efinition of : t = t = sin 0

Chapter 19: Electric Charges, Forces, and Fields ( ) ( 6 )( 6

Chapter 19: Electric Charges, Forces, and Fields ( ) ( 6 )( 6 Chapte 9 lectic Chages, Foces, an Fiels 6 9. One in a million (0 ) ogen molecules in a containe has lost an electon. We assume that the lost electons have been emove fom the gas altogethe. Fin the numbe