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A compilation by ELECTRIC FIELD COE, DC EM Name Completed on www.TheRafflesCafe.com | www.ThePhysicsCafe.com “How MARCH Can You Do in 1 Week? “ Package Page 2 www.TheRafflesCafe.com | www.ThePhysicsCafe.com www.ThePhysicsCafe.com 20 Name : _________________________ 1 Time: 25 mins (a) Define electric potential. (b) A helium nucleus with a charge of +3.20 1019 C and mass of 6.74 × 10–27 kg approaches a stationary gold nucleus of charge +1.26 1017 C along the line joining the two nuclei, as shown in Fig. 13. When the helium nucleus is at a distance of 1.77 × 10–12 m away from the gold 6 –1 nucleus, it is traveling at a speed of 7.0 × 10 m s . Assume that the helium nucleus and gold nucleus are point charges. Gold nucleus [1] 7.0 106 m s1 X Helium nucleus 1.77 1012 m Fig. 13 (i) 1. 2. Calculate the electric potential due to the gold nucleus at a distance of 1.77 × 10–12 m. [1] Hence, determine the electric potential energy of the helium nucleus when the separation of the helium nucleus and the gold nucleus is 1.77 × 10–12 m. [1] (ii) At point X, the helium nucleus comes to rest momentarily. Given that the gold nucleus remains stationary, find the distance of point X from the gold nucleus. [3] “How MARCH Can You Do in 1 Week? “ Package Page 3 www.TheRafflesCafe.com | www.ThePhysicsCafe.com (iii) If the gold nucleus recoils away from the helium nucleus, explain whether your answer to (b) (ii) will be larger, smaller or the same. [1] 2 An electron is directed into a uniform electric field at an angle of 300 to the vertical as shown in Fig. 14 below. Its initial speed is 1.0 × 106 m s─1. The parallel plates are arranged 10 cm apart in vacuum. The right plate is at a potential of +20 V relative to the left plate. The electron moves along the path as shown by the dotted line and hits the positive plate. The mass of an electron is 9.11 x 10−31 kg. e 1.0 × 106 m s ─1 30 0V 0 10 cm +20 V (a) Fig. 14 State the shape of the path followed by the electron. [1] (b) Find the magnitude and direction of the acceleration experienced by the electron. [2] (c) Show that the time taken for the electron to reach the positive plate is 6.26 10 8 s . (d) [2] Hence, find the minimum length of the plates required to stop the electron from leaving the uniform electric field. [2] “How MARCH Can You Do in 1 Week? “ Package Page 4 www.TheRafflesCafe.com | www.ThePhysicsCafe.com 3) “How MARCH Can You Do in 1 Week? “ Package Page 5 www.TheRafflesCafe.com | www.ThePhysicsCafe.com www.ThePhysicsCafe.com 18 Name : _________________________ 1 (a) Time: 25 mins P and Q are two identical conducting spheres each carrying a charge +Q. They are placed in a vacuum with their centres distance d apart as shown in Fig. 4.1. d P Q Fig. 4.1 Explain why the force F between them is not given by the expression F Q2 4 0d 2 …………………………………………………………………………………………… …………………………………………………………………………………………… ……………………………………………………………………………………………… (b) [2] Electric fields and magnetic fields may be represented by lines of force. Fig. 4.2 shows some lines of force. B A Fig. 4.2 (i) State whether the field strength at the vicinity of A and at the vicinity of B is constant, increasing or decreasing when measured in the direction from A towards B. at A: ……………………………………………………………………….. [1] at B: ……………………………………………………………………….. [1] “How MARCH Can You Do in 1 Week? “ Package Page 6 www.TheRafflesCafe.com | www.ThePhysicsCafe.com (ii) Explain why the field lines can never touch or cross. …………………………………………………………………………………… …………………………………………………………………………………… ……………………………………………………………………………… 2) [2] Two equally charged solid conducting spheres with small radii, of equal uniform mass m are hanged from the top plate of two parallel charged plates, with insulated strings of negligible mass. Each sphere has a charge of 3.2 1012 C “How MARCH Can You Do in 1 Week? “ Package Page 7 www.TheRafflesCafe.com | www.ThePhysicsCafe.com “How MARCH Can You Do in 1 Week? “ Package Page 8 www.TheRafflesCafe.com | www.ThePhysicsCafe.com 3) (a) Define electric potential energy at a point. [1] (b) The figure below shows the path of a proton nucleus. 1 1 p travelling head-on towards a uranium 235 92 U 1.5x10-14 m path of proton uranium nucleus By considering only the electrostatic repulsion, the distance of closest approach of the proton to the uranium nucleus is 1.5x10-14 m. Mass of proton is 1.67 1027 kg (i) Name the form of the energy to which the kinetic energy of the proton has been converted when it is at the distance of closest approach. [1] (ii) Calculate the initial speed of the proton, and state the assumption that you have made in the calculation. [4] (iii) In nuclear fission reactions, protons are not normally used to induce the reactions. Suggest an alternative particle that you would use to penetrate the nucleus and explain your choice. [2] “How MARCH Can You Do in 1 Week? “ Package Page 9 www.TheRafflesCafe.com | www.ThePhysicsCafe.com “How MARCH Can You Do in 1 Week? “ Package Page 10 www.TheRafflesCafe.com | www.ThePhysicsCafe.com www.ThePhysicsCafe.com 24 Name : _________________________ 1) Time: 25 mins The two lamps on a bicycle are powered by a small dynamo. The dynamo’s internal resistance is 20 and at one particular speed, the dynamo generates an e.m.f. of 6.0 V. Each lamp may be considered to have a constant resistance of 5.0 . (a) (b) 2) Calculate the current in each lamp if the lamps are connected (i) in series [1] (ii) in parallel [1] Calculate the power dissipated in each light bulb for (i) and (ii) [1] Fig below shows a circuit for measuring a small e.m.f. produced by a solar cell. 10 V 0.5 5.0 Solar cell V “How MARCH Can You Do in 1 Week? “ Package Page 11 www.TheRafflesCafe.com | www.ThePhysicsCafe.com (a) The galvanometer shows null deflection when the variable resistor is set to 300 . Determine the value of the e.m.f., V of the solar cell. [1] (b) Fig 3.2 shows the 5.0 resistor being replaced with a 1.2 m uniform resistance wire PQ of total resistance of 7.0 . The variable resistor remains at 300. 10 V 0.5 I Q P Solar cell V moveable contact R (i) Calculate the current I, when the galvanometer shows null deflection. [2] (ii) Calculate the distance from P that contact R must be connected to wire PQ such that the galvanometer shows null deflection. [3] (iii) Explain why, this circuit is not suitable for measuring the e.m.f. of the solar cell when the value of the e.m.f. of the solar cell is of the order of millivolts. [1] “How MARCH Can You Do in 1 Week? “ Package Page 12 www.TheRafflesCafe.com | www.ThePhysicsCafe.com 4 A potentiometer has a uniform resistance wire AB of length 1.00 m and resistance R. It is powered by a battery of e.m.f. 2.00 V and negligible internal resistance, as shown. The resistance of the connecting wires for the potentiometer circuit is represented by RW. RW 2.00 V R A B X (a) Y With a standard cell of e.m.f. 1.018 V, connected between X and Y, the balance length is found to be 51.2 cm of the wire. Determine the ratio (b) RW . [3] R When a dry cell is connected between X and Y, the balance length is 74.8 cm. Calculate the e.m.f. of this dry cell. [3] “How MARCH Can You Do in 1 Week? “ Package Page 13 www.TheRafflesCafe.com | www.ThePhysicsCafe.com 5 (a) Distinguish between resistance and resistivity of a conductor. [2] (b) A cell of e.m.f. 2.50 V and internal resistance R is connected to two uniform resistive wires in series as shown in Fig. 2.1. The wires are made of the same material but have different lengths and diameters. Wire AB is 50.0 cm long and has a diameter d, whereas wire BC is 30.0 cm long and has a diameter 0.30 d. The ammeter and connecting wires are assumed to have no resistance. 2.50 V A R A Show that B RAB 0.150 RBC “How MARCH Can You Do in 1 Week? “ Package C [1] Page 14 www.TheRafflesCafe.com | www.ThePhysicsCafe.com (c) A battery of e.m.f. 2.00 V and internal resistance r is connected across wire BC in parallel with another resistor of resistance r as shown in Fig 2.2. The galvanometer shows no deflection when the jockey J is at the midpoint of wire BC. 2.50 V A R A B C J 2.00 V r r (i) Show that VBC = 2.00 V (ii) Determine the internal resistance R of the 2.50 V cell if the ammeter shows a [2] reading of 0.400 A. [3] “How MARCH Can You Do in 1 Week? “ Package Page 15 www.TheRafflesCafe.com | www.ThePhysicsCafe.com www.ThePhysicsCafe.com 18 Name : _________________________ 1 Time: 25 mins The circuit in Fig. 18.1 makes use of a thermistor immersed in a water bath to monitor the temperature of the bath. The thermistor T is connected in series with a fixed resistor R of resistance 500 and a 3.0 V battery of negligible internal resistance. A T 3.0 V B R C o o When the temperature of the water bath is 80 C and 20 C, the potential difference across BC is 2.5 V and 0.5 V respectively. (a) Determine the resistance of T when the temperature of the water bath is (i) 80 oC resistance = [2] resistance = [2] (ii) 20 oC (b) State the variation of the resistance of the thermistor with its temperature. [1] (c) The circuit in Fig. 18.1 can be used to check that the temperature of the water bath is maintained below 80 oC. A student suggests connecting a 2.5 V light bulb across BC and if the temperature of the water bath is at 80 oC, the bulb will light up. State why his suggestion is not feasible. [2] “How MARCH Can You Do in 1 Week? “ Package Page 16 www.TheRafflesCafe.com | www.ThePhysicsCafe.com 2 r E Switch, S A RL An ammeter A of negligible resistance is connected in series with a variable load resistor of resistance RL to determine the electromotive force E and the internal resistance r of a cell (Fig. 20.1). The following values of current I are obtained for different values of RL: The graph of R against 1 is plotted as shown, with gradient = I 1.5085 and y-intercept = -0.573. I/A 0.590 3.00 0.420 4.00 0.330 5.00 0.270 6.00 0.230 Graph of R L ag 1/I 7 R = 1.5085 / I - 0.573 6 5 4 L RL / Ω 2.00 3 2 1 0 0 1 2 3 4 5 -1 (1/I) / A (a) Find the EMF of the battery and the internal resistance r. [2] (b) The circuit in Fig. 20.1 can be modified to vary the brightness of showroom lights by adding bulbs in parallel to the variable load resistance RL. Fig. 20.3 shows a simplified model of such a circuit. r E Switch, S A RL RB “How MARCH Can You Do in 1 Week? “ Package Page 17 www.TheRafflesCafe.com | www.ThePhysicsCafe.com (i) Resistances RL and RB may be combined and treated as a single load R. The resistance of the bulb RB remains constant at 4.00 Ω and maximum power delivered by the cell occurs when R = r. When the cell delivers maximum power, calculate 1. the value of RL. RL = Ω [2] current = A [2] power = W [2] 2. the current in the circuit. 3. the power dissipated in the cell. (ii) Although the cell is supplying maximum power to the combined external load, the light bulb is not at its brightest. Explain why. [1] 3 (a) The figure shows a cell of e.m.f. 2.0 V and internal resistance 0.20 connected in parallel to two identical lamps L1 and L2. The ammeters A1 and A2 in the circuit have negligible resistance and A2 reads 0.50 A. A1 A2 2.0 V 0.20 (i) L1 L2 Calculate the potential difference across L1. potential difference = …………V [2] “How MARCH Can You Do in 1 Week? “ Package Page 18 www.TheRafflesCafe.com | www.ThePhysicsCafe.com (ii) If another identical lamp L3 is connected in parallel with L1 and L2, explain whether the current in ammeter A1 remains the same, increases or decreases. [2] (b) Fig. 4.2 shows a circuit which is used to measure the emf of Cell Y. Cell Y A J B 8.0 Cell X, 2.00 V Fig. 4.2 Cell X has an e.m.f. of 2.00 V and negligible internal resistance. It is connected in series with a 8.0 resistor and resistance wire AB. The resistance wire AB has a length 100.0 cm and a resistance, 2.0 . (i) Calculate the potential difference across AB. potential difference = …………V [1] (ii) (iii) The movable contact J is now moved along AB. When the galvanometer indicates a zero reading, the length AJ is 30.0 cm. Calculate the e.m.f., in mV, of Cell Y. e.m.f.= ……..….. V [2] Without changing the length AB, suggest three modifications to the circuit of Fig. 4.2 that would cause the contact J to be closer to A when the galvanometer gives a zero reading. [2] “How MARCH Can You Do in 1 Week? “ Package Page 19 www.TheRafflesCafe.com | www.ThePhysicsCafe.com “How MARCH Can You Do in 1 Week? “ Package Page 20 www.TheRafflesCafe.com | www.ThePhysicsCafe.com www.ThePhysicsCafe.com 18 Name : _________________________ 1) (a) Time: 25 mins State what is meant by a field of force. [1] (b) Atoms of Neon-20 are ionised by the removal of one electron from each atom. These ions are accelerated through a potential difference of 1400 V. They are then injected into a region of space where there are uniform electric and magnetic fields acting in right angles to the original direction of motion of the ions. The region of magnetic and electric fields and polarities of the electric plates are shown in Fig 1.1. + + + + + + + + Region of uniform electric and magnetic fields Path of Neon ions - - - - - - - - Fig 1.1 “How MARCH Can You Do in 1 Week? “ Package Page 21 www.TheRafflesCafe.com | www.ThePhysicsCafe.com The electric field has field strength E and the flux density of the magnetic field is B. (i) State the charge of a Neon ion. Charge of a Neon ion: …………………………. [1] (ii) Calculate the speed of the Neon ions before they enter into the region of the electric and magnetic fields. Mass of Neon 20 atom can be assumed to be 20 X mass of 27 proton. Mass of proton = 1.66 10 kg Speed = …………………….. m s-1 (iii) (1) [3] State the direction of the electric force acting on a Neon ion when it enters into the shaded region. Direction of electric force: ……………………. [1] (2) (iv) Draw the direction of the magnetic field onto the shaded region in Fig 1.1 such that the Neon ions pass through the shaded region undeflected. The electric field strength E is 6.2 x 103 V m-1. Calculate the magnitude of the magnetic flux density so that the ions are not deflected in the region of the fields. Magnetic flux density = …………………… T (c) [1] [2] The mechanism by which the Neon atoms in (b) are ionised is changed so that each atom loses two electrons instead of just one. State the changes that occur in (i) the speed of the ions entering the region of the electric and magnetic fields in (b). [1] (ii) the path of the ions in the two fields. [1] “How MARCH Can You Do in 1 Week? “ Package Page 22 www.TheRafflesCafe.com | www.ThePhysicsCafe.com 2) A narrow beam of electrons at a speed of 3.2 × 107 m s─1 travels along a circular path in a uniform magnetic field of flux density, B, as shown in Fig. 3.1 below. B incident beam of electrons Fig. 3.1 (a) (i) Explain why the electrons undergo uniform circular motion. [3] ..………………………………………………………………………………...… ..…………………………………………………………………………………... ..………………………………………………………………………………...… ..………………………………………………………………………………… (ii) Show that the speed, v, of the electrons in the field is given by v Ber m where r is the radius of the circular path of the beam in the field. [2] (iii) The radius of the circular path of the beam in the field was found to be 25 mm. Determine the magnetic flux density of the field. Flux density = ….................... T [2] “How MARCH Can You Do in 1 Week? “ Package Page 23 www.TheRafflesCafe.com | www.ThePhysicsCafe.com 3) (a) A charged particle may experience a force in an electric field and in a magnetic field. State the difference between the forces experienced in the two types of field. .....................................………………………………………………………………………………………… [1] (b) A proton, travelling in a vacuum at a speed of 4.5 × 106 m s–1, enters a region of uniform magnetic field of flux density 0.12 T. The path of the proton in the field is a circular arc, as illustrated in Fig. 3.1. Fig 3.1 (i) State the direction of the magnetic field. .…………………………………..……………………………………………………… [1] (ii) Calculate the radius of the path of the proton, in terms of cm, in the magnetic field. 27 Mass of proton = 1.66 10 kg radius = ………………………… cm [3] (c) A uniform electric field is now created in the same region as the magnetic field in proton passes undeviated through the region of the two fields. (i) On Fig. 3.1, mark with an arrow labelled E, the direction of the electric field. Fig. 3.1, so that the [1] (ii) Calculate the magnitude of the electric field strength. electric field strength = ………………………… N C-1 [2] (d) Suggest why gravitational force on the proton has not been considered in the calculations in (b) and (c). .....................…………………………………..……………………………………………..…………… [1] “How MARCH Can You Do in 1 Week? “ Package Page 24 www.TheRafflesCafe.com | www.ThePhysicsCafe.com www.ThePhysicsCafe.com 28 Name : _________________________ 1) Time: 30 mins (a) Electrons from a filament source enter a region between the parallel plates after being accelerated by an electric field. Fig. 7.1 below shows the electrons travelling horizontally at a speed of 2.50 x 107 m s-1 entering the pair of parallel plates. +V 40 mm 7 2.5 x 10 m s -1 Fig. 7.1 0V (i) The electrons deviate by 30° on leaving the parallel plate of 80.0 mm long. The separation between the plates is 40.0 mm. Calculate the time taken for the electrons to traveling through the plates. time = ………………….. s (ii) Calculate the vertical component of the velocity when the electrons exit the parallel plates. vertical component of velocity = ……………… m s-1 (iii) [1] [2] Hence calculate the acceleration of the electrons. Given the mass of electron is 9.11 10 31 kg acceleration = ………………..m s-2 “How MARCH Can You Do in 1 Week? “ Package [1] Page 25 www.TheRafflesCafe.com | www.ThePhysicsCafe.com (iv) Calculate the p.d. V between the two plates. p.d. = ………………… V [2] (b) A magnetic field is applied to the region of the electric field in Fig. 7.1 so that the electrons pass straight through undeflected. (i) Indicate in words or sketch the direction of the magnetic flux density for Fig. 7.1 in the space below. [1] (ii) Calculate the magnetic flux density required to produce this effect. magnetic flux density = ………………… T [2] (c) The parallel plates in Fig. 7.1 are removed but the magnetic field is kept at the same value and direction. (i) Draw the path taken by the electrons in the magnetic field in the space below. (ii) Calculate the radius of curvature of these electrons. radius = ……………….. m (iii) [1] [2] Determine the speed of the electrons upon leaving the field. Explain your reasoning. ………………………………………………………………………………… ………………………………………………………………………………[2] 2) (a) Define magnetic flux density. “How MARCH Can You Do in 1 Week? “ Package Page 26 www.TheRafflesCafe.com | www.ThePhysicsCafe.com ....................................................................................................................................... ................................................................................................................................. [1] (b) Describe, by means of a well-labelled diagram, the motion of electrons moving at right angles in a uniform (i) electric field, .................................................................................................................................. ........................................................................................................................... [2] (ii) magnetic field. .................................................................................................................................. ........................................................................................................................... [2] (c) A rectangular strip of copper of dimensions 10 mm 5 mm 1 mm carries a conventional current I. A magnetic field B of flux density 1.0 T is applied in a direction perpendicular to the strip as shown in Fig. 4.1. 10 mm I P Q S R 5 mm 1 mm B 1.0 T Fig. 4.1 (i) Explain how a voltage is set up across side PQ with respect to SR. .................................................................................................................................. .................................................................................................................................. .................................................................................................................................. “How MARCH Can You Do in 1 Week? “ Package Page 27 www.TheRafflesCafe.com | www.ThePhysicsCafe.com .................................................................................................................................. .................................................................................................................................. ........................................................................................................................... [3] (ii) Calculate the voltage, given that the velocity of the electrons is 2.52 10 5 ms–1. voltage = ........................................ V [2] 3) (a) Define the tesla [1] (b) Fig. 4.1 shows an electric motor which is made up of a rectangular coil of wire of 150 turns. The coil is 0.20 m long and 0.12 m wide. The coil has a current of 0.32 A flowing through it and its plane is parallel to a field of magnetic flux density 0.36 T. magnetic field 0.12 m Y 0.20 m 0.32A X (i) Draw arrows on Fig. 4.1 to represent the directions of the magnetic forces acting on the coil. Label them F. [1] (ii) Calculate the magnitude of the magnetic force acting on one side of the coil. force = ………………………… N [1] (iii) Calculate the torque which is exerted on the coil. torque = ………………………… N m [1] “How MARCH Can You Do in 1 Week? “ Package Page 28