Electrostatics: Grade 12 Past Paper Questions

7.1 X is a point 0,025 m away from a +4 nC point charge. See the diagram below. 7.1.1 Draw the electric field pattern due to the +4 nC charge. 7.1.2 Calculate the magnitude of the electric field at point X. 7.2 Two identical neutral polystyrene balls A and B are suspended from a ceiling by insulated, light inextensible strings of equal length, as shown in the diagram below. Ball B is then given an initial negative charge, Qʙ, of unknown magnitude. The balls attract each other, touch and then repel each other. The balls come to rest with their centres 10 cm apart so that each string makes an angle of 9º with the vertical. See the diagrams below. 7.2.1 State Coulomb's Law in words. 7.2.2 Calculate the magnitude of the initial charge Qʙ given to ball B if the mass of each ball was 0,012 kg.

P is a +2 nC point charge. X is a point 6 cm away from charge P, as shown in the diagram below. 7.1 Calculate the magnitude of the electric field at X. Point charge S, with a charge of −2 nC, is placed 4 cm to the right of charge P, as shown in the diagram below. 7.2 Draw the resultant electric field pattern due to charges P and S. A third point charge T is placed 2 cm to the right of S, as shown in the diagram below. Point charge T experiences a net electrostatic force of 2,5 x 10⁻⁴ N to the left. 7.3.1 State Coulomb's law in words. 7.3.2 What is the polarity of charge T? Choose from POSITIVE or NEGATIVE. 7.3.3 Calculate the magnitude of charge T.

Two point charges, X and Y, are held 0,03 m apart, as shown in the diagram below. The charge of X is -7,2 x 10⁻⁹ C, while the charge of Y is +7,2 x 10⁻⁹ C. 7.1 State Coulomb's law in words. 7.2 Draw the net electric field pattern due to the two point charges. 7.3 Calculate the magnitude of the electrostatic force that Y exerts on X. A third point charge, Z, of unknown positive charge, is positioned 0,01 m to the left of point charge X on the line joining point charges X and Y, as shown in the diagram below. 7.4 Draw a labelled vector diagram to show the directions of the electric fields at the point where X is positioned. 7.5 The magnitude of the resultant electric field at the point where X is positioned is 4,91 x 10⁵ N·C⁻¹. Calculate the magnitude of charge Z.

Two small, charged spheres, R and S, are placed 120 mm apart in a vacuum, as shown in the diagram below. Sphere S has 7,5 x 10¹² electrons in excess and sphere R has a charge of +0,7 µC. Point P is 40 mm to the right of sphere R. 9.1 Define the term electric field at a point. 9.2 Draw a diagram to show the net electric field pattern around the two spheres if they had the same magnitudes of charges. 9.3 Calculate the: 9.3.1 Charge on sphere S. 9.3.2 Net electric field at point P.

7.1 A small neutral sphere acquires a charge of -1,95 x 10⁻⁶ C. 7.1.1 Were electrons ADDED TO or REMOVED FROM the sphere? 7.1.2 Calculate the number of electrons which were added or removed. 7.1.3 Define the term electric field at a point. 7.1.4 Calculate the magnitude of the electric field at a point 0,5 m from the centre of the charged sphere. 7.2 Two point charges, q₁ and q₂, are fixed 0,02 m apart. The magnitude of charges q₁ and q₂ is the same and q₁ is NEGATIVELY charged. The small charged sphere with the charge of -1,95 x 10⁻⁶ C is placed at point P, 0,03 m east of charge q₂, as shown in the diagram below. The sphere at point P experiences a net electrostatic force of 1,38 N west. Calculate the magnitude of the charge on q₂.

Four pith balls are charged. Ball A and ball D have unknown charges. Ball B has a charge of –2 x 10⁻³ C and ball C has a charge of +2 x 10⁻³ C. The effect of ball A when held above each of the isolated test tubes with each of the other charged pith balls, is shown in the diagram below. Ball B remains at the bottom of the test tube. Ball C moves up until it is 4 cm from ball A. Ball D moves up so that it is 2,4 cm from ball A. 8.1 State Coulomb's Law in words. 8.2 Identify the charge on ball A as POSITIVE or NEGATIVE. Explain the answer. 8.3 Draw a free-body diagram of ALL the forces that are exerted on ball A in diagram 2. 8.4 The net electrostatic force between ball A and ball C is Fₐᴄ. Calculate the charge on ball D if the force between A and D is the same as the force between A and C.

7.1 A small negative charge q placed at a fixed distance from charged sphere Q, experiences a force F, as shown in the diagram below. The charge q is now removed. Draw the electric field pattern for the charged sphere Q. 7.2 Sphere S is attached to the ceiling at point P by a light inextensible string. When sphere R, on an insulated stand, is brought close to sphere S they repel and sphere S comes to rest with the horizontal distance between the centres of the spheres equal to 0,03 m. Sphere R is directly below point P. The string makes an angle θ with the vertical, as shown in the diagram below. 7.2.1 State Coulomb's law in words. 7.2.2 Draw a labelled free-body diagram showing ALL the forces acting on sphere S when it is at rest. Sphere R has a charge of +6 nC. Sphere S has a charge +3 nC and a mass of 0,15 g. 7.2.3 Calculate angle θ.

Two small spheres P and S, carrying charges of +4 µC and +9 µC respectively, are placed 0,1 m apart. 7.1 State Coulomb's law in words. 7.2 Calculate the magnitude of the electrostatic force experienced by sphere S. X is a point r metres to the right of sphere P, as shown in the diagram below. 7.3 Define the term electric field at a point. 7.4 Calculate r if the net electric field at point X is zero. 7.5 The two spheres are brought into contact and returned to their original positions. 7.5.1 Were electrons transferred from sphere P to S or from sphere S to P when they were in contact? 7.5.2 At what distance from sphere P will the net electric field now still be zero?

The diagram below shows two identical metal spheres, R and S, each placed on an insulated stand. The spheres R and S carry charges of +9 µC and −5 µC, respectively. The spheres R and S are brought into contact for a while and then placed 30 cm apart. 7.1 Calculate the charge on each sphere immediately after separation. 7.2 Draw the resultant electric field pattern due to spheres R and S after separation. After R and S have been in contact and separated, a third sphere T of charge +1 µC is now placed between them, 10 cm from one sphere and 20 cm from the other, as shown in the diagram below. 7.3 Calculate the net electrostatic force experienced by T due to R and S. 7.4 Define the electric field at a point. 7.5 Calculate the net electric field at the location of T due to R and S.

QUESTION 7 A charged sphere M is suspended from a ceiling by a light inextensible, insulated string. Another charged sphere N, of mass 2,04 × 10⁻³ kg and carrying a charge of +8,6 × 10⁻⁸ C, hangs STATIONARY vertically below sphere M. The centres of the spheres are 0,3 m apart, as shown in the diagram below. 7.1 State Coulomb's law in words. 7.2 State whether the charge on sphere M is POSITIVE or NEGATIVE. 7.3 Draw a labelled free-body diagram for sphere N. 7.4 Calculate the magnitude of the charge on sphere M. 7.5 How does the electrostatic force that sphere M exerts on sphere N compare to that exerted by sphere N on sphere M with respect to: 7.5.1 Magnitude. 7.5.2 Direction. Point X is 0,1 m vertically below the centre of sphere N, as shown below. 7.6 Calculate the net electric field at point X.

1.6 The spectrum of helium emitted from a star moving away from Earth is compared to the spectrum of helium found on Earth. Which ONE of the following statements is CORRECT? The observed spectral lines from the moving star will have a … A. lower frequency and a longer wavelength. B. lower frequency and a shorter wavelength. C. higher frequency and a shorter wavelength. D. higher frequency and a longer wavelength. 1.7 The magnitudes of electric fields generated by different point charges are measured at a fixed point. For each measurement, the distance between this fixed point and the charges are the same. Which ONE of the following sketch graphs CORRECTLY shows the relationship between the magnitude of the electric field (E) and the magnitude of the charge (Q)?

1.7 Two identically charged spheres, X and Y, carry charges of +2q and −6q respectively. Sphere X experiences an electrostatic force F to the right when the distance between their centres is r. The spheres are brought into contact and are then returned to their original positions. Which ONE of the following represents the magnitude of the electrostatic force that sphere X experiences now? A. F. B. F/4. C. F/12. D. F/3. 1.8 In the circuit diagram below, R₁, R₂ and R₃ are identical resistors. The battery has negligible internal resistance. The power dissipated by R₁ is P. Which ONE of the following is the power dissipated by R₂?

1.3 Two blocks, P and Q, of masses m₁ and m₂ respectively, are held at rest on a frictionless horizontal floor with a compressed spring between them. When the blocks are released and the spring drops to the floor, block Q moves to the right with velocity v. Which ONE of the following represents the momentum of block P after the blocks are released? A. m₁v to the right. B. m₂v to the right. C. m₁v to the left. D. m₂v to the left. 1.4 The magnitude of the gravitational force that spheres X and Y exert on each other is F. The mass of sphere X is now doubled while the mass of sphere Y and the distance between the centres of the spheres remain the same. Which ONE of the following combinations is correct for the magnitude of the forces that the spheres now exert on each other? A. Force that X exerts on Y is F; force that Y exerts on X is F. B. Force that X exerts on Y is F; force that Y exerts on X is 2F. C. Force that X exerts on Y is 2F; force that Y exerts on X is F. D. Force that X exerts on Y is 2F; force that Y exerts on X is 2F.

QUESTION 6: A traffic officer is sitting in a police car which is travelling at a constant velocity. The siren of the police car emits sound waves of frequency 1500 Hz. A detector that is placed on the side of the road records a frequency of 1695 Hz. The police car takes 1,5 s to reach the detector. Take the speed of sound in air as 340 m·s⁻¹. 6.1 Name and state the phenomenon described above. 6.2 Write down ONE medical instrument that makes use of the phenomenon in QUESTION 6.1. 6.3 Calculate the distance between the police car and the detector. 6.4 Draw a graph of the frequency heard by the traffic officer sitting in the police car as it moves towards and away from the detector, versus time. Indicate the following on the graph: the frequency heard by the traffic officer; the time taken by the police car to reach the detector. QUESTION 7: Three point charges, X, Y and Z, with charges of -3 µC, +6 µC and +9 µC respectively, are placed on insulated stands as shown below. 7.1 State Coulomb's law in words. 7.2 Calculate the net force acting on point charge Z. 7.3 Point charges X and Y are brought into contact and then separated. Point charge X is returned to its original position, while point charge Y is removed. 7.3.1 In which direction did electrons flow? Choose from X to Y or Y to X. 7.3.2 Calculate the number of electrons transferred to or from point charge X. 7.3.3 Point T is placed between point charges X and Z. Calculate the distance between point charges X and T where the net electric field is equal to zero.

1.4 A ball is thrown vertically upwards into the air. Ignore the effects of air friction. The net force acting on the ball when the ball is at its highest point is ... A. Zero. B. Equal to the weight of the ball. C. Less than the weight of the ball. D. Greater than the weight of the ball. 1.5 Which ONE of the following statements is always true for inelastic collisions in an isolated system? A. Both momentum and kinetic energy are conserved. B. Both momentum and kinetic energy are not conserved. C. Momentum is conserved, but kinetic energy is not conserved. D. Kinetic energy is conserved, but momentum is not conserved. 1.6 An object moving horizontally at a constant velocity suddenly encounters a rough horizontal surface. The object continues to move over this rough surface. Which ONE of the following statements is correct? The net work done on the object during the motion over the rough surface is ... A. Zero. B. Positive. C. Negative. D. Constant. 1.7 The hooter of a car emits sound of constant frequency as the car moves away from a stationary listener. Which ONE of the following properties of the sound heard by the listener will NOT change? A. Speed. B. Frequency.

1.7 Two identical spheres, P and Q, carry charges of +q and –2q respectively. Sphere P exerts an electrostatic force of magnitude F on sphere Q. Which ONE of the following represents the magnitude of the electrostatic force exerted on sphere P by sphere Q? A. F/2. B. F. C. 2F. D. 4F. 1.8 In the circuit diagram shown below all the resistors are IDENTICAL. Ignore the internal resistance of the cell. Which voltmeter will have the HIGHEST reading when switch S is closed? A. V₁. B. V₂. C. V₃. D. V₄.

1.5 Consider the two spectrum diagrams below. Diagram 1 represents the spectrum of an element in a laboratory on Earth. Diagram 2 represents the spectrum of the same element from a distant star as observed from Earth. Which ONE of the following can be deduced from the spectra above? A. The star is moving towards Earth. B. The star is at rest relative to Earth. C. The star is moving away from Earth. D. Both the star and Earth are moving towards each other. 1.6 The diagram below shows the field lines for the combined electric field due to two small charged spheres P and Q. Which ONE of the combinations below correctly shows the polarity of spheres P and Q? A. Sphere P: negative; sphere Q: positive. B. Sphere P: negative; sphere Q: negative. C. Sphere P: positive; sphere Q: positive. D. Sphere P: positive; sphere Q: negative.

1.6 The absorption spectra of the same element surrounding both star A and star B are observed from Earth. The spectral lines for star B are more red-shifted than those for star A. How do the frequencies of the observed spectral lines and the speed of star B compare to that of star A? A. Frequencies higher, speed greater. B. Frequencies higher, speed smaller. C. Frequencies lower, speed greater. D. Frequencies lower, speed smaller. 1.7 R and S are two small charged spheres placed a distance apart. P is a point to the right of sphere S. Eᵣ and Eₛ are the electric fields at point P due to the charges on spheres R and S respectively. See the diagram below. Which ONE of the following combinations is CORRECT for the net charge on spheres R and S? A. Sphere R: positive; sphere S: negative. B. Sphere R: negative; sphere S: positive. C. Sphere R: negative; sphere S: negative. D. Sphere R: positive; sphere S: positive.

1.6 The ratio of the wavelength of sound produced by a stationary source (λₛ) to the wavelength of the sound detected by a listener (λₗ) is 1:1,09. The listener is moving at constant velocity. The frequency of the source is fₛ and the frequency detected by the listener is fₗ. Which ONE of the following combinations of fₗ and the movement of the listener is CORRECT? A. Greater than fₛ; towards the source. B. Greater than fₛ; away from the source. C. Less than fₛ; towards the source. D. Less than fₛ; away from the source. 1.7 R and S are two NEGATIVE point charges of equal magnitude. P is a point to the left of R. Point P and charges R and S are on the same horizontal line. Which ONE of the following vector diagrams, drawn to scale, of the electric fields Eᵣ due to R, and Eₛ due to S, at point P, is CORRECT?

1.7 In which graph below can the gradient be used to calculate Coulomb's constant? 1.8 Two charges of +2 nC and –2 nC are placed on a straight line. S and T are two points that are on the same straight line as shown in the diagram below. Which of the following represents the directions of the resultant electric field at S and T CORRECTLY? A. At S: right; at T: left. B. At S: left; at T: left. C. At S: right; at T: right. D. At S: left; at T: right.

1.7 Point charges with magnitudes q, 2q, 3q and 4q are placed in different electric fields. The force on each point charge is measured and the results are recorded in the table below: A. a charge of 4q experiences a force of 60 N. B. a charge of q experiences a force of 20 N. C. a charge of 2q experiences a force of 25 N. D. a charge of 3q. Which point charge experiences the greatest electric field strength? 1.8 Two identical light bulbs, P and Q, are connected as shown in the circuit diagram below. The internal resistance of the battery can be ignored. When switch S is closed, which combination best represents the effect on the ammeter reading and the brightness of bulb P: A. reading on ammeter increases, brightness of bulb P stays the same. B. reading on ammeter stays the same, brightness of bulb P increases. C. reading on ammeter stays the same, brightness of bulb P stays the same. D. reading on ammeter increases, brightness of bulb P increases. 1.9 The diagram below shows a coil in a magnetic field. When the coil is part of a DC motor, which ONE of the following must be connected to X and Y: A. split ring (commutator). B. slip rings. C. AC supply. D. soft iron core.

1.7 Two small identical spheres, each with mass m and charge +Q, are placed in a vertical cylinder. The spheres remain stationary when their centres are r metres apart, as shown in the diagram below. Ignore ALL frictional effects. Which ONE of the following expressions can be used to CORRECTLY calculate the distance r? A. √(kQ²/mg). B. √(kmg/Q²). C. √(Q²/kmg). D. √(mg/kQ²). 1.8 The kilowatt-hour (kWh) is a unit of … A. power. B. electric current. C. electrical energy. D. potential difference.