Huiswerk Hoofstuk 22 Elektriese velde Homework Chapter 22 Electric fields

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1 1 Huiswerk Hoofstuk Elektriese velde Homework Chapter Electric fields 8 th / 8 ste HRW 1, 5, 7, 10 (0), 43, 45, 47, 53 9 th / 9 de HRW ( N left, 30 N/C), 3, 8 (0), 11, 39, 41, 47, 49

2 Elektriese Velde Ladings en kragte Enige lading 1 stel elektriese veld in die omgewing rondom dit op. Chapter Electric Fields Charges and forces 1 1 Any charge 1 sets up an electric field in the space that surrounds it. 1 Grootte van : word bepaal deur grootte van 1 en afstand vanaf 1 1 Magnitude of : depends on magnitude of 1 and distance from 1 1 Rigting van : polariteit teken van 1 Plaas naby 1 1 het interaksie met deur die elektriese veld. 1 Direction : polarity of 1 Place near 1 1 interacts with through electric field. F 1 1

3 - Die elektriese veld Definieer elektriese veld by punt naby gelaaide voorwerp deur krag op positiewe toetslading 0, by daardie punt te meet. - The electric field Define electric field at point near charged object by measuring force on positive test charge 0 at that point. 3 F E = SI eenheid: NC -1 0 E = F 0 SI unit: NC -1 NB: Toetslading verander nie die oorspronklike veld nie! NB: Test charge does not alter the original field!

4 Elektriese veld Elektriese veld is n vektorveld By elke punt rondom gelaaide voorwerp, word daar n sekere grootte & rigting aangedui. Electric field Electric field is a vector field At each point around a charged object, there are a magnitude & direction indicated. 4

5 -3 Elektriese veldlyne -3 Electric field lines 5 Diagram van elektriese veld vir puntlading Diagram van elektriese veldlyne Diagram of electric field for point charge Diagram of electric field lines

6 Elektriese veldlyne -veldlyne dui kwalitatief die grootte en rigting van die netto -veld aan. Die veld wys in n rigting raaklynig aan die veldlyne by n gegewe punt. Die grootte van die -veld is eweredig aan die aantal veldlyne per eenheids area, loodreg op die lyne (m.a.w. die veldsterkte is eweredig aan die digtheid van die lyne.) Veldlyne begin altyd op n positiewe lading en eindig op n negatiewe lading. Veldlyne kan mekaar nooit kruis nie. Veldlyne is altyd loodreg op die oppervlak van n geleier. Electric field lines -field lines show ualitatively the magnitude and direction of the -field. The field points in a direction tangential to the field lines at a given point. The magnitude of the -field is proportional to the number of field lines per unit area, perpendicular to the lines. (i.e. field magnitude is proportional to the density of lines.) Field lines always start at a positive charge and end on a negative charge. Field lines can never cross. Field lines are always perpendicular to the surface of a conductor. 6

7 Elektriese veldlyne -veldlyne is gerig weg van positiewe lading en na negatiewe lading Electric field lines -field lines extend away from positive charge and toward negative charge 7 Vir puntladings is veldlyne gerig direk na of weg vanaf lading in n radiale rigting. For point charges, field lines are directed towards or away from charge in a radial direction.

8 Positiewe toetslading naby n groot, nie-geleidende plaat met n uniforme + lading aan die een kant. Positive test charge close to a large, non-conducting sheet with uniformly distributed + charge on one side. 8 Dipole/ Dipool

9 -4 Elektriese veld a.g.v. n punt lading -4 Electric field due to point charge 9 Rigting van F weg van as positief is en na as negatief is Grootte van veld: E F = = F 1 4πε = r 1 πε 0 0 r Direction of F away from if is positive and towards if is negative Magnitude of field: Rigting van E dieselfde as F vir positiewe lading Direction of E the same as F for positive charge

10 Superposisie beginsel Die resultante elektriese veld a.g.v. meer as een puntlading word gevind deur die beginsel van superposisie te gebruik. F0 = F01 + F0 + + F0 n E F 01 0 = F E = E + E... The resultant electric field due to more than one point charge is found by using the principle of superposition Superposition principle + F 0n 0 E n 10

11 Voorbeeld 1 Example 1 n Proton en n elektron vorm twee hoeke van n gelyksydige driehoek met sylengte m. Wat is grootte van die netto elektriese veld by die derde hoek? A proton and an electron form two corners of an euilateral triangle of side length m. What is the magnitude of their net electric field at the third corner?

12 Voorbeeld Example n Elekton word by elke hoek van n gelyksydige driehoek met sylengte 0 cm geplaas. Wat is die grootte van die elektriese veld by die middelpunt van een van die sye? An electron is placed at each corner of an euilateral triangle having sides of 0 cm long. What is the magnitude of the electric field at the midpoint of one of the sides? 1 - a a - -

13 Example 3 Voorbeeld 3 13 Wat is die groote en rigting van die elektrieseveld by die middelpunt van die vierkant indien = 10 nc en a = 5.0 cm is. What is the magnitude and direction of the electric field at the centre of the suare if = 10 nc and a = 5.0 cm.

14 -8 Puntlading in n eksterne elektriese veld -8 Point charge in an external electric field F 14 Gestel E word opgestel deur n sekere verspreiding van lading. Lading word dan geplaas in die eksterne E-veld. Die teken van moet in aanmerking geneem word. Elektrostatiese krag F wat op gelaaide deeltjie, in eksterne E- veld, inwerk, is gerig in rigting van E as positief is en in teenoorgestelde rigting as negatief is. F = E Suppose E is set up by some arrangement of charge. Charge is then placed in the external E-field. The sign of must be taken into account. Electrostatic force F acting on charged particle in external E- field, points in direction of E if is positive and in opposite direction if is negative.

15 Voorbeeld 4 Example 4 (a) Wat is die versnelling van n elektron in n univorme elektriese veld van N/C? (b) Hoe lank sal dit die elektron neem om vanuit rus een-tiende van die snelheid van lig te bereik? (c) Hoe vêr sal dit in daardie tyd beweeg? (a) What is the acceleration of an electron in a uniform electric field of N/C? (b) How long would it take for the electron, starting from rest, to attain one-tenth the speed of light? (c) How far would it travel in that time? 15

16 -5 Elektriese veld a.g.v. n elektriese dipool ladings, + en, afstand d uit mekaar uit. Elektriese dipool -5 Electric field due to an electric dipole charges, + and, separated by a distance d. Electric dipole 16 Bepaal die elektriese veld by punt P n afstand z van die middelpunt, waar z >> d (d.w.s z is baie groter as die afstand d vêr weg van dipool) Determine the electric field at point P a distance z from the center, where z >> d (i.e. z is much larger than the distance d far away from dipole E = E + E 1 = 4πε r ( + ) ( ) 1 o 1 4πε r ( + ) o ( ) 1 = ( ) ( ) 4πε ( z ½d ) 4πε ( z ½d ) E = 1 1+ z o o + d d 4πε z z o

17 E = ( ) ( ) 1 d 1+ d z 4πε z z o 17 Vir z >>d, kan die terme in hakkies uitgebrei word d.m.v. die binomiaal stelling: ( 1+ x) Om E te vereenvoudig, word terme tot eerste orde gehou: n For z >>d, then the terms in brackets can be expanded using the binomial theorem: nx n( n 1) x = < 1!! 1 for ( x 1) To approximate E, we keep terms up to first order: E d d 1 1 4πε o z z z E d 1 d = 4πε z z πε z o 3 o

18 Elektriese veld a.g.v. n elektriese dipool d = p Vektor hoeveelheid wat bekend staan as elektriese dipool moment. Rigting : + elektriese dipool E 1 πε o Electric field due to an electric dipole p z = electrical dipole 3 d = p 18 Vector uantity known as the electrical dipole moment. Direction : + Voorbeelde: Examples: CO: p = C m H O: p = C m KBr: p = C m

-8 n Dipool in n elektriese veld Sekere molekules het permanente dipoolmoment, wat n draaimoment sal ondervind indien dit in n E- veld geplaas word.

19 -8 n Dipool in n elektriese veld Sekere molekules het permanente dipoolmoment, wat n draaimoment sal ondervind indien dit in n E- veld geplaas word. -8 A dipole in an electric field Some molecules have permanent dipole moment that will experience a torue when placed in an E-field. 19 Draaimoment op dipool : Torue acting on dipole : τ = p E

Huiswerk Hoofstuk 23 Chapter 23 Homework

Huiswerk Hoofstuk 23 Chapter 23 Homework 8 th / 8ste HRW 1, 2(-72 N m 2 /C, 24 N m 2 /C, -16 N m 2 /C,, -48 N m 2 /C), 6, 11, 17, 18( 8. µc,12 µc,-5.3 µc), 22 (, 5.99 1 3 N/C), 27, 29, 35, 34, 37, 46(2.2