H213 Electric Fields - 2. Tutorial wSolutions (1718) (Updated 28 Feb)

9749 H2 Physics Tutorial w/ Solutions Topic 13: Electric Fields Page 1 of 22 Topic 13 Electric Fields Data Formulae electric potential, V = 4 o Q r Multiple Choice Questions 1 The diagram shows a non -uniform electric field near a positively charged and a negatively charged sphere. Four electrons, A, B, C and D, are shown at different positions in the field. On which electron is the direction of the force on the electron shown correctly? permittivity of free space, εo = 8.85  10–12 F m–1 (1/(36 π))  10–9 F m–1 elementary charge, e = 1.60  10–19 C unified atomic mass constant u = 1.66  10–27 kg rest mass of electron, me = 9.11  10–31 kg rest mass of proton, mP = 1.67  10–27 kg

9749 H2 Physics Tutorial w/ Solutions Topic 13: Electric Fields Page 2 of 22 2 The diagram shows the electric field near a point charge and two electrons X and Y. Which row describes the forces acting on X and Y? direction of force magnitude of force on X A radially inwards less than force on Y B radially inwards greater than force on Y C radially outwards less than force on Y D radially outwards greater than force on Y 3 The diagram below shows two small charged spheres P and Q of small mass which are hung by identical fine nylon threads from a fixed point X. It is found that, in equilibrium, the angle a is greater than the angle b. Which of the following statements must be correct? A The mass of P is less than that of Q. B The mass of P is greater than that of Q. C The charge of P is numerically smaller than that of Q. D The charge of P is numerically greater than that of Q. a b X P Q

9749 H2 Physics Tutorial w/ Solutions Topic 13: Electric Fields Page 3 of 22 4 Point charges, each of magnitude Q, are placed at three corners of a square as shown in the diagram. What is the direction of the resultant electric field at the fourth corner? 5 A charged particle is in the electric field between two horizontal metal plates connected to a source of constant potential difference, as shown. There is a force F on the particle due to the electric field. The separation of the plates is doubled. What will be the new force on the particle? A F/4 B F/2 C F D 2F 6 A particle has a charge of 4.8 × 10 –19 C. The particle remains at rest between a pair of horizontal, parallel plates having a separation of 15 mm. The potential difference between the plates is 660 V. What is the weight of the particle? A 1.1 × 10−23 N B 2.1 × 10−17 N C 2.1 × 10−15 N D 2.1 × 10−14 N +Q +Q – Q A B C D

9749 H2 Physics Tutorial w/ Solutions Topic 13: Electric Fields Page 4 of 22 7 Four charges are arranged at the corners of a square as shown. Point P is located at the centre of the square. The diagonal of the square is 8.0 cm. How much work is done by the field in bringing a −3.0 nC charge from infinity to point P without any change in its kinetic energy? A 270 μJ B 135 μJ C −135 μJ D −270 μJ 8 A small negatively charged particle P is balanced halfway between two horizontal plates where a potential difference of V is applied between the plates. When V is increased, P rises towards the upper plate. When V is decreased, P falls towards the lower plate. Which statement is correct? A The change of electric potential energy of the particle must equal the change in gravitational potential energy of the particle. B Increasing V increases both the gravitational and electric potential energy of the particle. C Decreasing V decreases both the gravitational and electric potential energy of the particle. D Decreasing V decreases the gravitational potential energy and increases th e electric potential energy of the particle. P +200 nC +300 nC −400 nC −500 nC P V

9749 H2 Physics Tutorial w/ Solutions Topic 13: Electric Fields Page 5 of 22 9 The electric potentials V are measured at distances x from P along a line PQ. The results are: V / V 13 15 18 21 23 x / m 0.020 0.030 0.040 0.050 0.060 The component along PQ of the electric field for x = 0.040 m is approximately A 250 V m-1 towards P B 250 V m-1 towards Q C 300 V m-1 towards P D 300 V m-1 towards Q 10 The diagram below describes a region in an electric field. Which of the following correctly describes the change in electric potential energy and force on an electron as it moves from X to Y? Potential Energy Force A Increases, then decreases Decreases, then increases B Increases Constant C Decreases Increases, then decreases D Decreases, then increases Constant 100V 50V +50V +100V 0V X Y

9749 H2 Physics Tutorial w/ Solutions Topic 13: Electric Fields Page 6 of 22 Structured Questions 11 (a) State what is meant by an electric field. (b) The electric field between an earthed metal plate and two charged metal spheres is illustrated in Fig. 11.1. Fig. 11.1 (i) On Fig. 11.1, label each sphere with (+) or (–) to show its charge. (ii) On Fig. 11.1, mark a region where the magnitude of the electric field is 1. constant (label this region C), 2. decreasing (label this region D). (c) Fig. 11.2 shows the configuration of two isolated conductors. Sketch, on Fig. 11.2, the electric field lines for the region of space between two-conductors. Fig. 11.2 – – – – – – – – – + + + It is a region of space where an electric charge experiences a force (due to other charged bodies). + – p C D

9749 H2 Physics Tutorial w/ Solutions Topic 13: Electric Fields Page 7 of 22 12 Two ions A and B are separated by a distance of 0.72 nm in a vacuum, as shown in Fig. 12.1. A has a charge of +4.8 × 1019 C and B has a charge of 3.2 × 1019 C. (a) Without making detailed calculations, draw labelled arrows on the figure to represent (i) the field EA at the point X due to A only, (ii) the field EB at X due to B only, (iii) the resultant field ER at X due to both charges. Fig. 12.1 (b) Sketch on the diagram lines representing the electric field caused by the two ions in the region within the rectangle. Include the field line passing through X. A B X EA EB ER

9749 H2 Physics Tutorial w/ Solutions Topic 13: Electric Fields Page 8 of 22 13 A molecule has its centre P of positive charge situated a distance of 2.8 × 10 –10 m from its centre N of negative charge, as illustrated in Fig. 13.1. Fig. 13.1 The molecule is situated in a uniform electric field of field strength 5.0 × 10 4 V m–1. The axis NP of the molecule is at an angle of 30° to this uniform applied electric field. The magnitude of the charge at P and at N is 1.60 × 10–19 C. (a) On Fig. 13 .1, draw an arrow at P and an arrow at N to show the directions of the forces due to the applied electric field at each of these points. (b) Calculate the torque on the molecule produced by the forces in (a). 14 Two fixed charges +1.0 C and 3.0 C are 10.0 cm apart. Determine a point where a third charge be located so that no net force acts on it? Since the 2 are unlike charges and the magnitude of the negative charge is larger, the neutral point must lie in the region beyond the positive charge. Let x be the distance from the positive charge. At the neutral point, Q QE E         6 6 2 2 2 2 2 2 1 0 10 3 0 10 4 4 0 100 0 1 3 2 0 2 0 1 0 0 137 0 0366 . . . . . . . m or . m (i nadmi s ib e) s l o o x x x x x x x                 Torque     19 4 10 o 24 1.60 10 5.0 10 2.8 10 sin30 1.12 10 Nm E perpendicularF d          

9749 H2 Physics Tutorial w/ Solutions Topic 13: Electric Fields Page 9 of 22 15 Fig. 15