Physical Sciences Electrostatics

Physical Sciences GRAD E 12 SELF STUDY GUIDE ELECTROSTATICS

TABLE OF CONTENTS Page 1. Introduction 2 2. How to use this self-study guide 3 3. Electrostatics 3.1 Mind map 4 3.2 Definitions and objectives 5–6 3.3 Content 7 – 24 3.4 Questions 25 – 37 4. Solutions to exercises 4.1 Multiple choice questions 38 4.2 Structured questions 39 - 45 5. Acknowledgement 46 6. References 47 1

1. Introduction The declaration of COVID-19 as a global pandemic by the World Health Organisation led to the disruption of effective teaching and learning in many schools in South Africa. The majority of learners in various grades spent less time in class due to the phased-in approach and rotational/ alternate attendance system that was implemented by various provinces. Consequently, the majority of schools were not able to complete all the relevant content designed for specific grades in accordance with the Curriculum and Assessment Policy Statements in most subjects. As part of mitigating against the impact of COVID-19 on the current Grade 12, the Department of Basic Education (DBE) worked in collaboration with subject specialists from various Provincial Education Departments (PEDs) developed this Self-Study Guide. The Study Guide covers those topics, skills and concepts that are located in Grade 12, that are critical to lay the foundation for Grade 12. The main aim is to close the pre-existing content gaps in order to strengthen the mastery of subject knowledge in Grade 12. More importantly, the Study Guide will engender the attitudes in the learners to learning independently while mastering the core cross-cutting concepts. 2

2. How to use this Self Study Guide? This booklet is aimed at summarising important aspects in the study of Electrostatics. It is not aimed at replacing the prescribed textbook and it must be used in conjunction with the textbook and other relevant study materials. The booklet combines the definitions that have been provided since Grade 10, to show how the topic progresses up to Grade 12. It includes the examination guidelines, to provide guidance on how far the learner should go in terms of mastering the content. Additionally, misconceptions are clarified for ease of understanding. The exercises provided in this booklet will not ensure sufficient practise; therefore, the learner should supplement them with additional practise. Also read the side notes as they assist in clarifying the content. 3

3. ELECTROSTATICS (Charges at rest) 3.1 Mind map Transferred between objects protons electrons ATOMS current ELEMENTS momentum Types: Like & Positive and unlike conserved Energy negative Attraction & CHARGE Electrostatics repulsion Magnetic fields Quantised Coulomb’s law Pattern strength Forces Newton 3rd law uniform Non- uniform Freebody diagram Parallel plates Point charges. Trigonometric ratios 4

DEFINITIONS It is a physical property of matter that causes it to experience a force Charge when kept in electromagnetic field. Principle of The net charge of an isolated system remains constant during any conservation of physical process e.g. two charges making contact and then separating. charge The total (net) electric charge of an isolated system remains constant in any physical process. Principle of charge All charges in the universe consist of an integer multiple of the charge quantization on one electron, i.e. 1,6 x 10-19 C Polarization The partial or complete polar separation of positive and negative electric charge in a system. A dipole. A way of representing an electric field. Arrows on the field lines indicate Electric field lines the direction of the field Electric field Is the region of space in which an electric charge experiences a force. The direction of the The direction that a positive test charge (+1C) would move if placed at electric field that point at a point Electric field at a The electrostatic force experienced per unit positive test charge placed point (E) at a point. The magnitude of the electrostatic force exerted by one point charge Q 1 on another point charge Q2 is directly proportional to the product of the Coulomb’s law two charges and inversely proportional to the square of the distance r between them. 5

3.2 Definitions and Objectives Objectives 6

3.3 Content 3.3.1 Study tips Electrostatics requires a thorough revision of Vectors. You must be able to identify the forces that are acting on the charges and draw free body diagrams. Newton’s third law applies in all force interactions. It is important to master Mathematical calculation of Trigonometric ratio of sin, cos and tan as Electrostatics involves triangles. You will be required to use Pythagoras theorem. Understand fields from grade 10 Magnetism. 3.3.2 Charge An atom is the basic unit of matter, it contains charges (protons and electrons). Protons are positively charged, and electrons are negatively charged. Bohrs’ atomic model of carbon Neutral atom Electrons are the ones which are removed and transferred to the other object. Charge is the fundamental quantities of electricity. It is fundamental to electricity as mass is to mechanics. It is associated with the atom and subatomic particles of material substances. All matter contains charges. The symbol of charge is (Q). The SI unit of charge is coulomb (C). Charge is conserved - the net charge in an isolated system remains constant during any physical interactions. Conversion scale: 1 micro coulomb (µC)= 1x10-6C Example: 1nano Coulomb (nC)= 1x10-9C 6 µC means 6 X 10-6C 1pico coulomb (ρC) = 1x10-12C 1 milli coulomb (mC) = 1x10-3C 7

3.3.3 Principle/law of conservation of charge- the total (net) charge of an isolated system remains constant in any physical process. Q1  Q2 Use the formula to apply the law of conservation of charge: Qnet , 2 Note: if there are three charges touching simultaneously, add them and divide by three (3) and not two (2) as in the given equation. Q1  Q2  Q3 Example: Qnet 3 Three metal spheres of equal size carry charges of -2 x 10-11 C, 5 x 10-11 C and -8 x 10-11 C respectively. They are brought into contact and then separated. What is the charge on each sphere after separation? Solution: Q1  Q2  Q3 Qnet 3 charge on each sphere  2 u 10 11  5 u 10 11  (8 u 10 11 ) Qnet 3 Q net 1.67 u 10 11 C Charge is quantised same as light. Quantised means charge is found in packets as eggs are sold in dozens, cold drinks in crates, etc. all charges are the multiples of the smallest charge, i.e., the charge of one electron is -1,6 X 10-19 C. Getting the number of electrons transferred or added, we use the formula: Q ne  qe  Q ne   1.6 u 1019 Using the previous example: Calculate the number of electrons transferred or removed from the charge. οܳ ൌ ܳ௙௜௡௔௟ െ ܳ௜௡௜௧௜௔௟ Q ne qe ିଵଵ ିଵଵ 3.30 u 10-12 ne 1.6 u 10 19 ൌ െͳǤ͸͹ ൈ ͳͲ െ ሺെʹ ൈ ͳͲ ሻ ne 2.63 u 107 electrons =ൌ ͵Ǥ͵Ͳ ൈ ͳͲିଵଶ ‫ܥ‬ Neutral charge- is an/a atom/material with equal number of protons and electrons. Example: In the diagram below the object contains four (4) protons and four (4) electrons 8

3.3.4 Types of charges x Positive charge-proton x Negative charge- electron A positively charged object has more protons than electrons and a negatively charged object has more electrons than protons. Example: Excess electrons Deficient electrons Note: In figure A electrons have been transferred to the object, and in figure B electrons have been removed. Charging involves the transference/movement of electrons from one object to another. 3.3.5 How to charge x By contact (friction) and x Polarization or Induction. Van de Graaf generator Use to generate charges. 9

Charging by contact Before Picture courtesy of pHet simulations After charging by contact Picture courtesy of pHet simulations 10

Polarization of charge Charging by induction Using the charged balloon to charge the neutral wall. https://phet.colorado.edu/sims/html/balloons-and-static-electricity/latest/balloons-and-static- electricity_en.html use the link to download offline free simulations. 11

We use an Electroscope: To detect whether an object is charged or not. And determine the sign of the charge on charged object. A placed next to a metal causes the negative charges to be polarised to the gold leaf. Then the because of like charges. 3.3.6 Coulomb’s law-Attraction and repulsion forces Like charges repel each other, i.e., positive and positive; or negative and negative. Diagram A Unlike charges attract each other, i.e., negative and positive. Diagram B Coulomb’s law NB: In both diagrams A and B, the objects exert equal but opposite Coulomb’s forces/electric/electrostatic force is one of the four forces on each other. Newton’s fundamental forces in nature. Others include: Electromagnetic third law. forces, weak and strong nuclear forces and gravitational force. All the four forces are examples of Electromagnetic forces are conservative forces. combination of electric and magnetic forces. They act from a distance. 12

Difference: gravitational force is only an attractive force, but electrostatic force is both attractive and repulsive forces. Definition in words: Coulomb’s law states that, the electrostatic force exerted by one point charge (Q 1) on another point charge (Q2) is directly proportional to the product of the two charges and inversely proportional to the square of the distance (r) between them. F – magnitude of force Directly proportional: when magnitude Mathematically of charges increases, the force r – distance between charges increases, vice versa. Q1 and Q2 – magnitude of Inversely proportional: when the charges distance between charges increases, the force decreases, vice versa Formular will F help you to remember the definition. FDQ1Q2 Definition Graphically 1 F F FD r2 F r2 Q1 Q2 1 r2 Coulomb’s law Do not confuse this laws. Newton law of universal gravitation Similarities: both product of the quantities, inversely proportional to the square of the distance Differences: Different constant- Coulomb is k and Newton is G Coulomb: attraction and repulsion. Newton is attraction only. Newton- masses Coulomb- charges Newton – attraction only 13

Example 1: What will be the magnitude of the electrostatic force between two charges Q1 and Q2 when the magnitude of both charges is doubled? FDQ1Q2 FnewD 2Q1 2Q2 FnewD 4Q1Q2 FnewD 4 F Example 2: If charge Q1 is halved and charge Q2 is four times. What will be the magnitude of the electrostatic force? FDQ1Q2 FnewD 1 2 Q1 4Q2 FnewD 2Q1Q2 FnewD 2 F Example 3: If the distance between two charges Q1 and Q2 is halved. What will be the force on each charge? 1 FD r2 1 FnewD ( 2 r )2 1 1 1 FnewD u 2 1 4 r FnewD 4 F Example 4: one of the charges is doubled and the distance is made a third. What will be the force? 2Q1Q 2 2 Q1Q 2 FnewD D u 2 D18F ( 13 r ) 2 19 r Example 5: Two charges of magnitude +6nC and -3nC are placed 30mm apart. What is the magnitude and direction of the force acting on 6nC charge? kQ1Q 2 9 u 109 u 6 u 109 u 3 u 109 F 1.8 u 10 4 N Attraction to right r2 (301000) 2 When substituting the charges in NB: Identify attraction and the equation do not include the repulsion. Draw free body Convert 30 mm to metres by negative sign of the charge diagrams. dividing by 1000. 14

Charges in 1 dimension (1D): Identifying forces and free body diagram FA on B FC on A FC on B FA on C FB on C FB on A Charges in 2 dimension (2D): Identifying forces and free body diagram Net force acting on A Net force acting on B FB on A FB on A FC on B FA on B FC on A FC on B Net force acting on C FC on A FA on Fnet FA on B FB on A Fnet FC on A FB on C use Pythagoras Use sine rule to or trigonometric Fnet ratio to calculate calculate the values. FB on A required value. FA on Use Pythagoras or trigonometric C FB on C ratios to calculate. Use sine rule. Use Pythagoras to resolve the forces. or or or or 15

Example 6.1- Multiple Choice question Answer: P1 is charged, therefore when in contact with P2 the electrons are going to be transferred. Charging by contact is taking place. After charging, distribution of Q1  Q2 charges is going to take place according to this equation, Q meaning both 2 will acquire same (positive or negative) and equal charge. Force of repulsion will take place. So option C, D and B are close, but option C has a different sign, therefore option D is the correct One. Option A the problem is the unequal magnitude. Option B, is also repulsion but the problem is the unequal part. 16

Example 6.2: Draw a free body diagram for all the forces acting on sphere P1 in diagram 2 above. Exercise 6.3: do yourself: Draw a free body diagram for all the forces acting on sphere P2 in diagram 2 above. Answer: For you to do. Example 8: 8.1 kQ1Q 2 F r2 9 u 109 u 6 u 10 6 u 8 u 10 6 F (0.2) 2 F 10.8 N 17

repulsion Like charges Unlike charges attraction resultant 8.2 Draw the vectors first. Show Answer: the correct direction. Sphere Y has a positive charge and sphere Z is negative, therefore sphere Y will be attracted towards Z, downwards. Sphere X is positive; therefore, sphere Y will be repelled away from sphere X to the right. Vector diagram will be: Fnet FZ on Y FX on Y 18

8.3 We use the Theorem of Pythagoras to calculate the force exerted by charge Z on sphere Y. 2 2 2 Complete a Fnet FZ .on.Y  FX .on.Y FZFZ onon Y triangle of 2 15.20 2 FZ .on.Y  10.8 2 forces. FX on Y FZ .on.Y 10.70 N FX on Y=10.8N kQY Q Z F r2 is the force which 9 u 109 u 8 u 10 6 u Qz sphere Y exert on sphere Z. 10.70 0.302 When using Coulomb’s law, we Qz 0.00001336875 must use the charge of Y with Z to Qz 1.34 u 10 5 C get charge of Z. 19

3.3.7 Electric fields We know magnets have magnetic fields. We define magnetic fields as a region in which a magnetic object will experience a force. Gravitational field is a region in which a mass will experience a force. The force of attraction and repulsion charges exert on each other is because of the electric field interaction. Electric field is defined as the region in space in which an electric charge will experience a force. Electric fields like magnetic field are represented by a pattern of imaginary field lines. Properties of electric field lines Field lines start on positive charge and ends on negative charge. Fields lines never cross or touch each other. Field lines are closer together in regions where the field is stronger and further apart in regions where the field is weak (non-uniform fields). Field lines are parallel where the field is uniform. Electric fields are continuous. Field lines begin and end perpendicularly to the charged surface. drawing electric field lines Point charge Positive point charge negative point charge Electric fields point AWAY from a point charge Do not forget to draw the Electric fields arrows. point TOWARDS a point charge 20

Interaction of point charges due to their Electric fields Attraction-unlike charges Repulsion 3.3.8 Electric field at a point Electric field at a point is the electrostatic force experienced per unit positive test charge placed at that point. Symbol E Unit is N.C-1 E is a vector quantity Mathematically: F- the force experienced by q. q- the positive test charge. When electric field at a point Increases, the force increases. Electric fields are non-uniform. Increasing the magnitude of a test charge, the electric field at a point The Electric field decreases as the test decreases charge moves away from the point charge. Test charge experiences different forces at different distances. 21

Example 9: Calculate the magnitude of the force exerted on a charge of 8P placed in an electric field at a point of 4 X 104N.C-1. F Convert into Coulomb E q F 4 u 104 8 u 106 F 0.32 N Coulomb’s law and Electric field at a point both have forces, another formula to calculate Electric field at a point. kQq F F 2 E r q All experiences the same Force (Newton’s 3rd law), therefore, equating the two equations: kQq Eq r2 test charge q is cancelling out. kQ ?E r2 Q is the point charge. Example 9: Calculate the electric field at a point at 5mm from a point of charge of  5PC . Convert 5mm to m. kQ 5 / 1000 E r2 Convert 9 u 109 u 5 u 10 6 microcoulomb to E (5 u 10 3 ) 2 Coulomb E 1.8 u 109 N .C 1 22

Charges in 1 Dimension: for Electric field at a point F Since E what happens in the Force also happens in the Electric field at a point. q EC at B EC at A EA at B EB at C EA at C EB at A E of A and B are all to the right. E of A is to the right Enet E B.at . A  EC .at . A and E of B is left kQBatA kQCatA Choose right as Enet   positive. r2 r2 Enet E A.at .C  E B.at .C kQ kQCatB Enet  AatB  kQ kQ 1,5 2 (1,5  0,5) 2 Enet  AatC 2  ( BatC ) r r2 kQAatC kQ Distance between A and C, add Enet  CatB AB and BC (1,5  0,5) 2 0,5 2 Not Examinable for enrichment purposes. Charges in 2 Dimension: for Electric field at a point: E EB EB EC Enet Use cosine and sine rule 23

Example 10 Direction of Fields of both A and B at point P are to the right. Choose Right as positive. 10.1 Distance between sphere B and point P is 0.7 – 0.40= 0.3m Check: Sphere A field lines will be directed to the right, and sphere B field lines are to the right. Therefore, we choose right as positive Remember not to substitute the negative sign in the formula. ? Enet E A  EB kQA kQB Enet  2 r2 r 9 u 10 u 1.5 u 10 6 9 u 109 u 2 u 10 6 9 Enet  0.42 0.32 Enet 284375N .C 1right 10.2 F E q F 284375 3.0 u 10 9 F 8.53 u 10 4 N 24

3.4 Questions 3.4.1 Multiple Choice Question 1 1.1 1.2 25

1.3 1.4 Two charged spheres of magnitudes 2Q and Q respectively are placed a distance r apart on insulating stands. If the sphere of charge Q experiences a force F to the east, then the sphere of charge 2Q will experience a force ... A B Cc D F to the west. F to the east. 2F to the west. 2F to the east. P, Q and R are three charged spheres. When P and Q are brought near each other, they experience an attractive force. When Q and R are brought near each other, they experience a repulsive force. Which ONE of the following is TRUE? A B P and R have charges with the same sign. P and R have charges with opposite signs. P, Q and R have charges with the same sign. P, Q and R have equal charges. 26

1.5 Two charges, + Q and — Q, are placed a distance d from a negative charge — q. The charges, + Q and — Q, are located along lines that are perpendicular to each other as shown in the diagram below. ° D 2) Which ONE of the following arrows CORRECTLY shows the direction of the net force acting on charge — q due to the presence of charges + Q and - Q? A ————> B a ¢ \ D + 27

1.6 1.7 Two charged particles are placed a distance, r, apart. The electrostatic force exerted by one charged particle on the other is Fe Which ONE of the graphs below CORRECTLY represents the relationship between the electrostatic force, Fe, and the square of the distance, Pr, between the two charges? A B we ira P P c D Ww Wwe Ww Wwe Pr Pr Three identical positive point charges, Qi, Q2 and Q3, are initially situated on a smooth flat table at the corners of a right-angled triangle. The diagram below shows the charges as viewed from above. a® Which ONE of the following diagrams shows the direction in which Q2 will move as a result of the electrostatic forces exerted by Q; and Q3 on it? A \. 5 ©14 28

1.8 1.9 The magnitude of the electrostatic force on a charge Q, due to another charge Q:2 is F. Both charges are now doubled without changing the distance between them. The magnitude of the new electrostatic force on Q, will be: A oF 2 B 2F C 4F D oF Two small identical metal spheres, on insulated stands, carry charges -q and +3q respectively. When the centres of the spheres are a distance d apart, the spheres exert an electrostatic force of magnitude F on each other. mM d ——> The spheres are now made to touch and are brought back to the same positions as before. The magnitude of the electrostatic force which the spheres now exert on each other, in terms of F, is: 4 =F A 3 1 B 3F 1 “F c 2 D 3F 29

1.10 Particle P has charge Q and particle R has charge 2Q. They are separated by a small distance, r. Which ONE of the statements below about the electrostatic forces, Fpr, which P exerts on R and Frp, which R exert on P, is CORRECT? A Fer= %Frp B Fer = Fre C Fer = 2Frp D- Fer=—Frp 30

3.4.2 Structured Questions Question 2 31

Question 3 Two identical negatively charged spheres, A and B, having charges of the same magnitude, are placed 0,5 m apart in vacuum. The magnitude of the electrostatic force that one sphere exerts on the other is 1,44 x 10'N. 0,5m @---------------- 22-22-22 ° A B 3.1 State Coulomb's law in words. (2) 3.2 Calculate the: 3.2.1 | Magnitude of the charge on each sphere (4) 3.2.2 | Excess number of electrons on sphere B (3) 3.3 P is a point at a distance of 1 m from sphere B. 05m — '¢—_4m ——> @-+--------+----- gene ER ' A B P 3.3.1. What is the direction of the net electric field at point P? (1) 3.3.2 Calculate the number of electrons that should be removed from sphere B so that the net electric field at point P is 3 x 10*N-C" to the right. (8) [18] 32

Question 4 A very small graphite-coated sphere P is rubbed with a cloth. It is found that the sphere acquires a charge of + 0,5 uC. 4.1 Calculate the number of electrons removed from sphere P during the charging process. Now the charged sphere P is suspended from a light, inextensible string. Another sphere, R, with a charge of — 0,9 uC, on an insulated stand, is brought close to sphere P. As a result sphere P moves to a position where it is 20 cm from sphere R, as shown below. The system is in equilibrium and the angle between the string and the vertical is 7°. Now the charged sphere P is suspended from a light, inextensible string. Another sphere, R, with a charge of — 0,9 uC, on an insulated stand, is brought close to sphere P. As a result sphere P moves to a position where it is 20 cm from sphere R, as shown below. The system is in equilibrium and the angle between the string and the vertical is 7°. 17° ! | 20 cm PO Gert rrrrrnn R Pp 4.2 Draw a labelled free-body diagram showing ALL the forces acting on sphere P. 4.3 State Coulomb's law in words. 4.4 Calculate the magnitude of the tension in the string. (3) (3) (5) [13] 33

Question 5 Two identical spherical balls, P and Q, each of mass 100 g, are suspended at the same point from a ceiling by means of identical light, inextensible insulating strings. Each ball carries a charge of +250 nC. The balls come to rest in the positions shown in the diagram below. Ceiling ! | 0°/20° ! P Q 5.1 In the diagram, the angles between each string and the vertical are the same. Give a reason why the angles are the same. (1) 5.2 State Coulomb's law in words. (2) 5.3 The free-body diagram, not drawn to scale, of the forces acting on ball P is shown below. T I I | ! Fe WIFg Calculate the: 5.3.1 Magnitude of the tension (T) in the string (3) 5.3.2 Distance between balls P and Q (5) [11] 34

Question 6 A sphere Q,, with a charge of -2,5 uC, is placed 1 m away from a second sphere Qo, with a charge +6 uC. The spheres lie along a straight line, as shown in the diagram below. Point P is located a distance of 0,3 m to the left of sphere Q,, while point X is located between Q, and Q2. The diagram is not drawn to scale. -2,5 uC +6 UC P Q xX Q, ~oanao ae SEEDERS Se —0,3 m—>« 1m > 6.1 Show, with the aid of a VECTOR DIAGRAM, why the net electric field at point X cannot be zero. (4) 6.2 Calculate the net electric field at point P, due to the two charged spheres Q; and Qe. (6) [10] 35

Question 7 7.1 In an experiment to verify the relationship between the electrostatic force, Fr, and distance, r, between two identical, positively charged spheres, the graph below was obtained. 1 GRAPH OF Fe VERSUS P 030 025 Zz 0,020 w 2 0,015 0,010 ,005 0 1 2 3 | 4 5 6 zz (m’) 7.1.1 State Coulomb's law in words. (2) 7.1.2 Write down the dependent variable of the experiment. (1) 7.1.3 What relationship between the electrostatic force Fe and the square of the distance, r’, between the charged spheres can be deduced from the graph? (1) 7.1.4 Use the information in the graph to calculate the charge on each sphere. (6) 36

7.2 A charged sphere, A, carries a charge of — 0,75 uC. 7.24 Draw a diagram showing the electric field lines surrounding sphere A. (2) Sphere A is placed 12 cm away from another charged sphere, B, along a straight line in a vacuum, as shown below. Sphere B carries a charge of +0,8 uC. Point P is located 9 cm to the right of sphere A. i 12cm i —0,75 uC | P | 40,8 uC i = nee go Qe A: ' ' cm ' B 7.2.2 Calculate the magnitude of the net electric field at point P. (5) [17] 37

4. Solutions 4.1 Multiple Choice Question 1 1.1 A 1.2 1 1 1 1 A ED 2 D 2 D 2D E r ( 2r ) 4r 4 1.3 A Newton’s third law. 1.4 B 1.5 C 1.6 B 1.7 C 1.8 C FD 2Q2QD 4F 1 1.9 B FD1q3qD 3F .......F 1q1qD1F .....FD F 3 1.10 D Newton’s third law 38

4.2 Structured Questions Question 2 Right: both charges have equal magnitude but R has a smaller r therefore force exerted will be bigger. 39

2.6 Force experienced v per unit positive charge ~ placed at that point. 27 OPTION 1 F 135 E=-vs Y= 1,35 x 10° N-Ctv q 1x10 (3) OPTION 2 kQ / _ (9x10°)(2x10*) r? (0,1)? kQ _ (9x10°)(2x10*) r? (0,2)? Enet = 1,8 x 10° - 4,5 x 10° = 1,35 x 10°N-C1v (3) OPTION 3 F e=fy=_18 Y= 1,8 x 10° N-C* q 1x10" F =o 045 =4,5x 10° N-Ct q 1x10 Enet = 1,8 x 10° - 4,5 x 10° = 1,35 x 10° N-C1v E, = Y= 1,8 x 10° N-C" right E, = = 4,5 x 10° N-C" left (3) [19] Question 3 3.1 The net electrostatic force on a charged particle due to the presence of another charged particle is directly proportional to the product of the chargesvand inversely proportional to the square of the distance between them v 3.2 _ KQ,Q, 321 Fea vo 9 2 144x197 = @x10 0" v (0,5) Q=2x10° Cv (4) 3.2.2 Q=nev 2x10 = n(1,6x10"%) v n= 1,25 x10 electrons (3) 40

3.3 3.3.1 Left(west) ¥ 3.3.2 Take right as positive Enet = Ea + Esv v y 9 6 9 (3x10) = -(2%10°12*10*) , (9*10")i (45) (1) Qhina = 4,22 x 10° Cv Q=ne 4,22 x10° = n(1,6x1 0-8) v ny = 2,64 x10 ~ electrons v electrons removed Notes / Aantekeninge No. electrons should be removed =n; — nj allocate the 1 mark for the subtraction = (2,64 x10"? +1,25 x10") v (8) = 3,89 x10" electronsv [18] Question 4 41 Q n=— e ~ 05x10° 1,6x10°° n= 3,13 x 10" Velectrons (3) 4.2 TIFy Fe Pp wi Fg Accepted labels/Aanvaarde benoemings w F,/ F,,/ weight / mg / gravitational force T Fry / tension Fe Electrostatic force/F c/ Coulombic force/F q /Freer (3) 4.3 The magnitude of the electrostatic force exerted by one point charge (Q1) on another point charge (Qz2) is directly proportional to the product of the (magnitudes of the) charges and inversely proportional to the square of then distance (r) between them. vv 41

4.4 OPTION 1/OPSIE 1 Q,Q Fe=k a v Tsin6/(Tcos®) = Fe 9 6 6 “T sin7/(Tcosa3°yv = (9x10°)(0.5x10°)(09x 10%) ¥ (0,2) ¥ “.T =0,83NY (Accept) (5) [15] Question 5 5.1 The magnitude of the charges are equalv/ The balls repel each other with the same/identical force or force of equal magnitudev (1) 5.2 The electrostatic force of attraction between two point charges is directly proportional to the product of the charges “and inversely proportional to the square of the distance between them. v (2) 5.3 5.3.1 Tcos20° = ww =mg = (0,1)(9,8)” = 0,98 N <.T = 1,04 NY (3) 5.3.2 POSITIVE MARKING FROM 7.3 Fotectrostatic= Tsin20°V kQ,Q, Y= (1,04)sin20° r kQ,Q, = 0,356 r 9 -9 -9 (9x10 25010 \(250x10°) 7 _ 0,356v r <1 = 0,0397 m ¥ (5) [11] 42

Question 6 6.1 Ea: X OR x —------ <==>=9--------. _------«—Far_¢, For Ea2 Vectors Eq: and Eq in the same directionY ¥ Correct drawing of vectors Eq: and Eqaav¥ The fields due to the two charges add up because they come from the same direction. Hence the field cannot be zero. (4) 62 E=kov Q _ (9x 10°)(2,5 x 10°) % Exsuc =k>= 250 000 N.C" to the left r (0,3)? 9 -6 Eouc = Ko aa <31 952,66 N.C" to the left Ep = Eoyc + E.2suc ¥ = 31 952,66 + 250 000 = 281 952,66 N.C” vto the left v (6) [10] Question 7 7.1.1 The (magnitude of the) electrostatic force exerted by one (point) charge on another is directly proportional to the product of the charges v and inversely proportional to the square of the distance between their (centres) them. ¥ (2) (1) 7.1.2 Fe/Electrostatic force v 7.1.3 The electrostatic force is inversely proportional to the square of the distance between the charges Vv OR The electrostatic force is directly proportional to the inverse of the square of the distance between the charged spheres (charges). ¥ OR F at v r2 OR They are inversely proportional to each other (1) 43

1 mark for using slope/ 7.1.4 | OPTION 1 Slope = AF. _ (0,027 -0)/, al (66-0) 2 = 4,82 x 10° N-m? Slope = Fer = kKQ1Q2 = kQ’?v 4,82 x 10° v=9 x 10° Q?2v “.Q=7,32x10"C v OPTION 2 Accept any pair of points on the line _KAQ ) r? F (9x10°)Q?v ( )vwyv Q=7,32x10"Cv (v= Examples 9 24 (0,005) ¥ = (9 x10" JQ" (1)vv Q=7,45x107C Vv 9 2 (0,027) ¥ = ower v ( 56 Q=7,32x107CVY yy (4,76 x 10° - 5 x 10°) (7,32 x 107 — 7,45 x 107 C) (6) 7.2 Criteria for drawing electric field: Kriteria vir teken van elektriese veld: Marke/Punte Direction /Rigting v Field lines radially inward/Veldlyne radiaal inwaarts v 44

7.2.2 kQy r? Take right as positive/Neem regs as positief 9 -6 Eng = (2% 10°0.75x10°) / (0,09 = 8,33 x 10° N-C" to the left/na links 9 6 Eps = (9x10 \(0,8 x 10 iy (0,03 = 8 x 10° N-C" to the left/na links Enet = Epa + Epc E= = 5 6 = [-8,33 x 10° + (- 8 x 10°)] v 1 mark for the addition of same signs/ = -8,83 x 10° 1 punt vir optelling van dieselfde tekens = 8,83 x 10°N-C'v Take left as positive/Neem links as positief Take left as positive/Neem links as positief ~ (9x 10°0,75x10*) / (0,09 = 8,33 x 10° N-C" to the left/na links Eps = (9x 10° (0,8 x 10° y (0,03) = 8 x 10° N-C" to the left/na links Enet = Epa + Epc Epa = 1 mark for the addition of same signs/ 7 38 xX ig + 0x10 Lv 1 punt vir optelling van dieselfde tekens = 883x . (5) [17] 45

5 ACKNOWLEDGEMENTS The Department of Basic Education (DBE) gratefully acknowledges the following officials for giving up their valuable time and families and for contributing their knowledge and expertise to develop this resource booklet for the children of our country, under very stringent conditions of COVID-19: Writer: Mr Sello Matube (Subject Specialist, PED: NW) Reviewers: Ms Marisa Smit, Mr Padmara Sathiyamma, Dr FK Owusu, M Koelman and Sunette von Moltke DBE Subject Specialist: Ms JSK Maharaj (Veena) The development of the Study Guide was managed and coordinated by Ms Cheryl Weston and Dr Sandy Malapile 6 References Physics Workbook 5 NWU Physical Sciences Std 10 Brink Jones 46

MMe / Vi Mer Y ISBN: 978-1-4315-3524-8 High Enrolment Self Study Guide Series > basic education This publication is not for sale. Bee etn © Copyright Department of Basic Education REPUBLIC OF SOUTH AFRICA www.education.gov.za| Call Centre 0800 202 993 |