Electrostatics: Grade 11 Past Paper Questions

1.7 Two identical conducting spheres carrying charges Q and −2Q are placed r metres apart. The electrostatic force acting on each sphere is F. The spheres are brought into contact and are then separated so that the distance between them remains r metres. Which ONE of the following is the magnitude of the electrostatic force that the spheres exert on each other after they are separated? A. F/2. B. F/4. C. F/8. D. F.

A third sphere S, of unknown charge, is placed 10 cm to the right of sphere R, as indicated in the diagram below. The net electrostatic force acting on sphere P due to spheres R and S is 6,6 N to the right. 7.4 Determine the: 7.4.1 Electrostatic force that sphere S exerts on sphere P 7.4.2 Charge on sphere S.

QUESTION 7. Three charged spheres, A, B and C, with charges of −4 nC, +7 nC and +10 nC respectively, are placed on rubber stands as shown below. 7.1 Can metal stands be used instead of rubber stands? Write down only YES or NO. Give a reason for the answer. 7.2 State Coulomb's law in words. 7.3 Calculate the net force acting on charge C. A and B are brought into contact and then separated. Charge A is returned to its original position while charge B is removed. 7.4.1 In which direction did the charge flow? Choose from A to B or B to A. 7.4.2 Calculate the number of electrons transferred to or from charge A.

7.5 A charged sphere A carries a charge of −0,65 μC. It is placed 10 cm away from another charged sphere B, which carries a charge of +0,8 μC, along a straight line in a vacuum. Point P is located 7 cm to the right of sphere A. 7.5.1 Define electric field at a point. 7.5.2 Draw electric field lines on sphere A. 7.5.3 Calculate the magnitude of the net electric field at point P.

QUESTION 5. Two small, identical positively charged spheres, A and B, are suspended from the ceiling at point C by non-conducting threads as shown below. 5.1.1 Draw a labelled closed vector triangle showing all the forces acting on sphere A. Include TWO angles in the triangle. 5.1.2 If the mass of each sphere is 1,5 g, calculate the magnitude of the electrostatic force acting on sphere A. 5.1.3 Calculate the magnitude of the electric field at sphere A due to sphere B if the charge on each sphere is 4,80 nC.

QUESTION 5. Two identical charged particles, R and S, are positioned 0,4 m apart along a straight line in a vacuum. Particle R has a charge of 3×10⁻⁶ C, while particle S has a charge of −5×10⁻⁶ C, as illustrated in the diagram below. 5.1 State Coulomb's law in words. 5.2 Calculate the magnitude of the electrostatic force that particle S exerts on particle R. Point P is x metres to the right of R, with R, P and S lying on a straight line. The electric field at P due to S is three times that due to R. 5.3 Calculate x. The net electric field at point P due to both particles R and S is 2,07×10⁶ N·C⁻¹ to the right. 5.4 Determine the electrostatic force exerted on an electron placed at point P.

QUESTION 7. A metal sphere P, which was initially neutral, is given a charge of −8 μC. 7.1 Determine the number of electrons added to P to obtain a charge of −8 μC. Sphere R, carrying a charge of 5 μC, is placed 20 cm to the right of sphere P along a straight line. Point x is located 5 cm to the right of sphere R, as shown in the diagram below. 7.2 Define the term electric field at a point in words. 7.3 Calculate the net electric field at point x. A third sphere S, of unknown charge, is placed 10 cm to the right of sphere R, as indicated in the diagram below. The net electrostatic force acting on sphere P due to spheres R and S is 6,6 N to the right. 7.4 Determine the: 7.4.1 Electrostatic force that sphere S exerts on sphere P 7.4.2 Charge on sphere S.

QUESTION 7. Three charged spheres, A, B and C, with charges of −4 nC, +7 nC and +10 nC respectively, are placed on rubber stands. 7.1 Can metal stands be used instead of rubber stands? Write down only YES or NO. Give a reason for the answer. 7.2 State Coulomb's law in words. 7.3 Calculate the net force acting on charge C.

7.4 Spheres A and B are brought into contact and then separated. Charge A is returned to its original position while charge B is removed. 7.4.1 In which direction did the charge flow? Choose from A to B or B to A. 7.4.2 Calculate the number of electrons transferred to or from charge A.

7.5 A charged sphere A carries a charge of −0,65 μC. It is placed 10 cm away from another charged sphere B, which carries a charge of +0,8 μC, along a straight line in a vacuum. Point P is located 7 cm to the right of sphere A. 7.5.1 Define electric field at a point. 7.5.2 Draw electric field lines on sphere A. 7.5.3 Calculate the magnitude of the net electric field at point P.

QUESTION 7. 7.1 Two spheres P and Q, placed on insulated stands, carry charges of +5 μC and −8 μC respectively. 7.1.1 Explain why the charges are placed on insulated stands. The charges are brought into contact and are then separated. 7.1.2 Are electrons transferred from P to Q or from Q to P during contact? Give a reason for the answer. 7.1.3 Calculate the number of electrons transferred. 7.1.4 Name and state the law used in the calculation in QUESTION 7.1.3. 7.2 R is a point charge of magnitude +6 nC. 7.2.1 Draw the electric field pattern for charge R. 7.2.2 State Coulomb's law in words.

QUESTION 3. A student conducts an experiment to investigate the relationship between the resultant force on an object, and acceleration. The experiment is set up using a trolley on an inclined runway, and a ticker timer that makes 50 dots every second. 3.1 Calculate the period of the ticker timer. When the trolley is released from the top of the runway, it moves down the slope and the following ticker tape is produced. 3.2 Briefly explain why the dots on the tape are initially close together. The slope of the runway is adjusted so that the dots become evenly spaced. 3.3 Was the ramp angle INCREASED or DECREASED? 3.4 What is the magnitude of the resultant force now acting on the trolley? 3.5 The trolley is now accelerated by first using one rubber band, then two rubber bands and finally three rubber bands. The rubber bands are stretched to the same extent each time. The three sets of results are plotted on a velocity-time graph shown below. 3.5.1 Which graph represents the results when THREE rubber bands were used? Choose from A or B. Give a reason for the answer. 3.5.2 Sketch a graph to show the relationship between the acceleration of the trolley and the force (in rubber band units) acting on the trolley.

1.5 The acceleration due to gravity on the surface of Earth is g. Which ONE of the following is the gravitational acceleration on another planet which has HALF the mass of Earth and ONE-QUARTER of Earth's radius? A. 2g. B. 4g. C. 8g. D. 16g. 1.6 A small sphere, carrying a constant charge, is placed r metres from a fixed point, P. The electric field E at P is measured for different values of r. Which of the following graphs correctly shows the relationship between the electric field E at P and r²? (Four E-versus-r² graphs are given as options.)

QUESTION 6 A rocket, with its fuel, has a mass of 20 000 kg on the surface of Earth. The rocket is launched vertically upwards and its mass decreases uniformly as the fuel burns. At a height of 6,4 × 10⁸ m above the surface of Earth, the rocket's mass DECREASES by 5000 kg. 6.1 State Newton's law of universal gravitation in words. 6.2 Calculate the weight of the rocket on the surface of Earth. 6.3 Determine the percentage reduction in the rocket's weight when it is 6,4 × 10⁸ m above the surface of Earth. The rocket's mass decreased by 25% as it ascends from the ground to 6,4 × 10⁸ m above the surface of Earth. 6.4 Explain why the percentage reduction in the rocket's weight is considerably larger than the percentage reduction in the rocket's mass. QUESTION 7 A metal sphere P, which was initially neutral, is given a charge of −8 μC. 7.1 Determine the number of electrons added to P to obtain a charge of −8 μC. Sphere R, carrying a charge of 5 μC, is placed 20 cm to the right of sphere P along a straight line. Point X is located 5 cm to the right of sphere R, as shown in the diagram below. 7.2 Define the term electric field at a point in words. 7.3 Calculate the net electric field at point X.

1.7 Two bodies, X and Y, of mass M and m respectively, exert a force F on each other when they are a certain distance apart. The mass of one of the bodies is doubled and the distance between their centres is halved. What is the new force that the bodies exert on each other, in terms of F? A. 8F B. 16F C. 4F D. 2F. 1.8 The distance between two charges, Q₁ and Q₂, is r. The force exerted by the spheres on each other is F. Both charges are now doubled without changing the distance between them. The magnitude of the electrostatic force on Q₁ will be: A. 4F B. ½F C. 2F D. ¼F. 1.9 Which one of the following diagrams indicates the direction of magnetic fields and how it is determined with a test charge around charged spheres correctly?

1.10 A negative charge Q is placed at a distance of 5d from another charge R, as shown in the diagram below. (The answer options give different combinations of the ratio of the charges and the sign of the charge on R.) QUESTION 2 A heavy object is lifted using two ropes and two pulleys, as shown in the diagram below. The two pulleys are a distance X apart. The force FA, in rope A, is 530 N and the force FB, in rope B, is 1240 N. Rope A makes an angle of 60° with the horizontal and rope B makes an angle of 20° with the vertical. 2.1 Define the term resultant vector. 2.2 Explain why the vector diagram of force FA, force FB and the weight will NOT be a closed vector diagram. 2.3 Calculate the: 2.3.1 Vertical component of FA. 2.3.2 Horizontal component of FA.

1.6 The graphs P, Q, R and S drawn below show a relationship between the force of attraction that two masses exert on each other and the inverse of the square of the distance between their centres. In which graph will the product of their masses be the largest? A. P. B. Q. C. R. D. S. 1.7 The force of attraction between two charges q₁ and q₂ is F. If the distance between the charges is made four times smaller, then the new force of attraction will be ... A. 0,5F. B. 1,78F. C. 2,5F. D. 16F.

QUESTION 6. The mass of planet Jupiter is 300 times the mass of Earth and its radius is 11 times larger than that of Earth. An astronaut has a mass of 120 kg. 6.1 State Newton's law of universal gravitation in words. 6.2 What will the weight of the astronaut be on the surface of Jupiter? QUESTION 7. 7.1 Two spheres P and Q, placed on insulated stands, carry charges of +5 μC and −8 μC respectively. 7.1.1 Explain why the charges are placed on insulated stands. The charges are brought into contact and are then separated. 7.1.2 Are electrons transferred from P to Q or from Q to P during contact? Give a reason for the answer. 7.1.3 Calculate the number of electrons transferred. 7.1.4 Name and state the law used in the calculation in QUESTION 7.1.3.

7.2 R is a point charge of magnitude +6 nC. 7.2.1 Draw the electric field pattern for charge R. S is a point charge of magnitude −9 nC placed 25 mm to the right of R. Z is a point x mm east of point charge S. Point charges R and S, and point Z lie on the same line. 7.2.2 State Coulomb's law in words. 7.2.3 Calculate the magnitude of the electrostatic force that charge R exerts on charge S. The net electric field at Z is 7,66×10⁴ N·C⁻¹ west. 7.2.4 Calculate the value of x in metres. QUESTION 8. A bar magnet moves horizontally towards a solenoid. 8.1 State Faraday's Law of electromagnetic induction in words.

1.4 Two charged objects repel each other with a force F when they are separated by a distance d. The distance between the same two charges is reduced to half. The new force, in terms of F, will now be... A. ¼F B. ½F C. 2F D. 4F. 1.5 The diagram below shows two light bulbs, P and Q, connected in series to a battery. If bulb P glows brighter than bulb Q, then the... A. resistance of bulb P is greater than that of bulb Q. B. resistance of bulb P is smaller than that of bulb Q. C. current through bulb P is smaller than that through bulb Q. D. current through bulb P is greater than that through bulb Q.

1.3 Two objects of masses 2m and m are arranged as shown in the diagram below. Which of the following changes will result in the largest increase in the gravitational force the two objects exert on each other? A. Double the mass of each object. B. Double the larger mass and double the distance between their centres. C. Double the larger mass and half the distance between their centres. D. Triple the smaller mass and half the distance between their centres. 1.4 Two charges, +Q and −Q, are each 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. 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? (Four directional-arrow diagrams are given as options.)

QUESTION 1. 1.1 Consider the vector diagram below: W, X, Y, Z. Which ONE of the following vectors is the resultant of the other three? A. W B. X C. Y D. Z. 1.2 The forces acting on an object are in equilibrium. Consider the following statements: (i) The object could be stationary (ii) The object could be moving at a constant velocity (iii) The acceleration of the object is zero. Which of the above statements is/are true? A. (i) only B. (ii) only C. (i) and (iii) only D. (i), (ii) and (iii). 1.5 The acceleration due to gravity on the surface of Earth is g. Which ONE of the following is the gravitational acceleration on another planet which has HALF the mass of Earth and ONE-QUARTER of Earth's radius? A. 2g B. 4g C. 8g D. 16g. 1.6 A small sphere, carrying a constant charge, is placed r metres from a fixed point, P. The electric field E at P is measured for different values of r. Which of the following graphs correctly shows the relationship between the electric field E at P and r²? 1.7 Two identical conducting spheres carrying charges Q and −2Q are placed r metres apart. The electrostatic force acting on each sphere is F. The spheres are brought into contact and are then separated so that the distance between them remains r metres. Which ONE of the following is the magnitude of the electrostatic force that the spheres exert on each other after they are separated? A. F B. F/2 C. F/8 D. F/4. QUESTION 2. A box is lifted vertically upwards at CONSTANT VELOCITY using two light, inextensible strings, P and Q. The strings pass over frictionless pulleys attached to a horizontal ceiling and are attached to the box at point X, as shown in the diagram below. The tension in string P, which makes an angle of 50° with the ceiling, is 200 N. String Q makes an angle of 40° with the ceiling. Ignore the effects of air resistance and assume that the box does not rotate while being lifted. 2.1 What is meant by a closed vector diagram? 2.2 Draw a fully labelled closed vector diagram representing all forces acting on the box. Indicate any TWO angles. 2.3 Calculate: 2.3.1 The magnitude of the tension in string Q 2.3.2 The mass of the box.

QUESTION 1: MULTIPLE-CHOICE QUESTIONS. 1.1 The statement below refers to vector and scalar quantities: (i) A vector has magnitude and direction, while a scalar has magnitude only. (ii) A scalar quantity can always be added to a vector quantity. (iii) Force is an example of a vector quantity, while distance is an example of a scalar quantity. Which of the above statements is/are TRUE? A. (i) only B. (i) and (ii) only C. (i) and (iii) only D. (i), (ii) and (iii). 1.3 A net force F is applied on an object of mass m kg and causes an acceleration of a m·s⁻². When the net force F on the same object is doubled, the resulting acceleration, in m·s⁻², will be... 1.4 A 1 kg mass is pulled along a frictionless slope, inclined at an angle, by a force shown in the sketch below. Which ONE of the following equations can be used to calculate the magnitude of the normal force (N)? A. N = (1)(9,8) sin θ B. N = F − (1)(9,8) cos θ C. N = F + (1)(9,8) cos θ D. N = (1)(9,8) cos θ. 1.7 The distance between two charges, Q₁ and Q₂, is r. The force exerted by the spheres on each other is F. Both charges are now doubled without changing the distance between them. The magnitude of the electrostatic force on Q₁ will be: A. 4F B. ½F C. 2F D. ¼F. 1.8 Two bodies, X and Y, of mass M and m respectively, exert a force F on each other when they are a certain distance apart. The mass of one of the bodies is doubled and the distance between their centres is halved. What is the new force that the bodies exert on each other, in terms of F? A. 8F B. 16F C. 4F D. 2F. QUESTION 2. A heavy object is lifted using two ropes and two pulleys, as shown in the diagram below. The two pulleys are a distance X apart. The force Fₐ, in rope A, is 530 N and the force F_B, in rope B, is 1 240 N. Rope A makes an angle of 60° with the horizontal and rope B makes an angle of 20° with the vertical. 2.1 Define the term resultant vector. 2.2 Explain why the vector diagram of force Fₐ, force F_B and the weight will NOT be a closed vector diagram. 2.3 Calculate the: 2.3.1 Vertical component of Fₐ 2.3.2 Horizontal component of Fₐ. 2.4 Calculate the maximum weight that force Fₐ and force F_B will be able to lift from the ground. Show ALL calculations. 2.5 Explain why the rope and pulley system will be less effective if the distance X between the pulleys is increased.

QUESTION 1. 1.1 Two forces P and Q act at a point O. As the angle θ between P and Q varies, the MAXIMUM and MINIMUM resultant forces are 13 N and 3 N respectively. The magnitudes of the two forces are: A. 3 N and 10 N B. 16 N and 10 N C. 8 N and 5 N D. 10 N and 7 N. 1.2 A passenger standing in a moving bus moves forward when the bus suddenly stops. This can best be explained by A. Newton's First law of motion B. Newton's Second law of motion C. Newton's Third law of motion D. Newton's law of Universal gravitation. 1.3 A learner sits on a chair. What is the reaction force to her sitting on the chair? A. Force that the learner exerts on the chair. B. Weight of the learner. C. Force that the chair exerts on the learner. D. Force that the learner exerts on Earth. 1.5 A car, moving to the right along a rough horizontal surface, is brought to rest by a constant net force. If the motion to the right is taken as positive, which ONE of the following acceleration versus time graphs is correct for the motion of the car? 1.6 The graphs P, Q, R and S drawn below show a relationship between the force of attraction that two masses exert on each other and the inverse of the square of the distance between their centres. In which graph will the product of their masses be the largest? A. P B. Q C. R D. S. 1.7 The force of attraction between two charges q₁ and q₂ is F. If the distance between the charges is made four times smaller, then the new force of attraction will be... A. 0,5F B. 1,78F C. 2,5F D. 16F. 1.8 The north pole of a bar magnet is pushed into a solenoid, as shown in the sketch below. The polarity of X on the solenoid and the direction of flow of the induced current through the solenoid will be... 1.9 The ampere second (A·s) is the unit for A. Current strength B. Quantity of charge C. Resistance D. Potential difference. 1.10 Which ONE of the following graphs represents the relationship between the total electrical energy transferred (W) and the electric current (I) in the element of a kettle? The resistance of the element and the time for which the current flows are constant. QUESTION 2. Three forces Fₐ, F_B and F_C act on a point O in the directions shown in the diagram below. The magnitudes of Fₐ and F_C are 44 N and 31 N respectively. The magnitude of F_B is unknown. The forces are NOT drawn to scale. 2.1 Define the term resultant vector. The resultant of the three forces is 26,69 N at an angle of 25,82° to the horizontal, and lies in the first quadrant. 2.2 Calculate the magnitude of F_B. 2.3 Determine θ.

7.2.3 Calculate the magnitude of the electrostatic force that charge R exerts on charge S. The net electric field at Z is 7,66×10⁴ N·C⁻¹ west. 7.2.4 Calculate the value of x in metres. QUESTION 8. A bar magnet moves horizontally towards a solenoid. 8.1 State Faraday's Law of electromagnetic induction in words. The graph below shows the change in magnetic flux (ΔΦ) versus the change in time (Δt) as the bar magnet moves through the solenoid. 8.2 Use the graph to calculate the rate of change of magnetic flux linked to the coil. 8.3 Calculate the magnitude of the EMF induced across the coil if the coil has 120 turns. 8.4 State TWO ways by which the induced EMF in the coil can be increased.

4.2 A spaceship, with its engines switched off, is moving towards Earth. The mass of the spaceship is 1250 kg. 4.2.1 State Newton's Law of universal gravitation in words. 4.2.2 Calculate the distance between the spaceship and the centre of Earth when Earth exerts a force of 2458 N on the spaceship. QUESTION 5. Two small, identical positively charged spheres, A and B, are suspended from the ceiling at point C by non-conducting threads as shown below. 5.1.1 Draw a labelled closed vector triangle showing all the forces acting on sphere A. Include TWO angles in the triangle. 5.1.2 If the mass of each sphere is 1,5 g, calculate the magnitude of the electrostatic force acting on sphere A. 5.1.3 Calculate the magnitude of the electric field at sphere A due to sphere B if the charge on each sphere is 4,80 nC.

QUESTION 1. 1.1 Two forces, F₁ and F₂, act simultaneously at a point. The resultant force is 17 N when they act in the same direction, and 5 N when they act in opposite directions. The magnitude of the two forces are: A. 14 N and 3 N B. 11 N and 6 N C. 5 N and 12 N D. 10 N and 7 N. 1.2 A person stands on a bathroom scale that is calibrated in newton, in a stationary elevator. The reading on the bathroom scale is W. The elevator now moves downward with a constant acceleration of ¼g, where g is the gravitational acceleration on Earth. What will the reading on the bathroom scale now be? A. ¼W B. ¾W C. W D. 5/4 W. 1.3 Two objects of masses 2m and m are arranged as shown in the diagram below. Which of the following changes will result in the largest increase in the gravitational force the two objects exert on each other? A. Double the mass of each object. B. Double the larger mass and double the distance between their centres. C. Double the larger mass and halve the distance between their centres. D. Triple the smaller mass and halve the distance between their centres. 1.4 Two charges, +Q and −Q, are each 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. 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? 1.5 The diagram below shows a magnet that is moved towards a solenoid. Which ONE of the following combinations are CORRECT? A. North, X to Y B. North, Y to X C. South, X to Y D. South, Y to X. 1.6 Which ONE of the following graphs best represents the relationship between the electrical power (P) dissipated by a resistor and the potential difference (V) across the resistor if the resistance of the resistor remains constant? 1.7 Which ONE of the following is the unit of measurement for the rate of flow of charge? A. Coulomb B. Ampere C. Volts D. Watts. QUESTION 2. Two forces act simultaneously on a small boat in a flat part of a river: the motor exerts a force of 1 200 N at an angle of 40° north of east; the river current exerts a force of 800 N in a northerly direction. The boat is at point O. 2.1 Define the term resultant vector. 2.2 Using an accurate scale drawing, determine the magnitude and direction of the resultant force acting on the boat. Use the scale 1 cm : 200 N.