Download 1. This question is about forces on charged particles in electric and

1. This question is about forces on charged particles in electric and magnetic fields. The diagram shows two parallel plates situated in a vacuum. One plate is at a positive potential with respect to the other. + Path of positively charged particle – A positively charged particle passes into the region between the plates. Initially, the particle is travelling parallel to the plates. (a) On the diagram, (i) draw lines to represent the electric field between the plates. (3) (ii) show the path of the charged particle as it passes between, and beyond, the plates. (2) (b) An electron is accelerated from rest in a vacuum through a potential difference of 750 V. (i) Determine the change in electric potential energy of the electron. ........................................................................................................................... ........................................................................................................................... ........................................................................................................................... (2)
1 (ii) Deduce that the final speed of the electron is 1.6 × 10 7 m s –1 . ........................................................................................................................... ........................................................................................................................... ........................................................................................................................... (2) The diagram below shows a cross­section through a current­carrying solenoid. The current is moving into the plane of the paper at the upper edge of the solenoid and out of the plane of the paper at the lower edge. There is a vacuum in the solenoid. Current into plane of paper × × × × × × × × × × × × × × × × × × × × × × × × × × × Current out plane of paper (c) (i) Sketch lines to represent the magnetic field inside and at each end of the solenoid. (4) (ii) A positively charged particle enters the solenoid along its axis. On the diagram, show the path of the particle in the solenoid. (1) An electron is injected into a region of uniform magnetic field of flux density 4.0 mT. The velocity of the electron is 1.6 × 10 7 m s –1 at an angle of 35° to the magnetic field, as shown below. 7 –1 1.6 × 10 m s 35° Direction of magnetic field
2 (d) (i) Determine the component of the velocity of the electron normal to the direction of the magnetic field. ........................................................................................................................... ........................................................................................................................... (2) (ii) Describe, making calculations where appropriate, the motion of the electron due to this component of the velocity. ........................................................................................................................... ........................................................................................................................... ........................................................................................................................... ........................................................................................................................... ........................................................................................................................... (4) (iii) Determine the component of the velocity of the electron along the direction of the magnetic field. ........................................................................................................................... ........................................................................................................................... (1) (iv) State and explain the magnitude of the force on the electron due to this component of the velocity. ........................................................................................................................... ........................................................................................................................... ........................................................................................................................... (2)
3 (e) With reference to your answers in (d), describe the shape of the path of the electron in the magnetic field. You may draw a diagram if you wish. ..................................................................................................................................... ..................................................................................................................................... (2) (Total 25 marks) 3. This question is about the force between current­carrying wires. Diagram 1 below shows two long, parallel vertical wires each carrying equal currents in the same direction. The wires pass through a horizontal sheet of card. Diagram 2 shows a plan view of the wires looking down onto the card. eye
sheet of card diagram 1 (a) (i) diagram 2 Draw on diagram 1 the direction of the force acting on each wire. (1) (ii) Draw on diagram 2 the magnetic field pattern due to the currents in the wire. (3)
4 (b) The card is removed and one of the two wires is free to move. Describe and explain the changes in the velocity and in acceleration of the moveable wire. ..................................................................................................................................... ..................................................................................................................................... ..................................................................................................................................... ..................................................................................................................................... ..................................................................................................................................... (3) (Total 7 marks) 5. This question is about emf and internal resistance. A dry cell has an emf E and internal resistance r and is connected to an external circuit. There is a current I in the circuit when the potential difference across the terminals of the cell is V. V r I (a) E State expressions, in terms of E, V, r and I where appropriate, for (i) the total power supplied by the cell; ........................................................................................................................... (1) (ii) the power dissipated in the cell; ........................................................................................................................... (1) (iii) the power dissipated in the external circuit.
5 ........................................................................................................................... (1) (b) Use your answers to (a) to derive a relationship between V, E, I and r. ..................................................................................................................................... ..................................................................................................................................... ..................................................................................................................................... (2) The graph below shows the variation of V with I for the dry cell. 1.6 1.5 1.4 1.3 1.2 1.1 1.0 0.90 0.80 V / V 0.70 0.60 0.50 0.40 0.30 0.20 0.10 0.0 0.0 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.0 1.1 1.2 1.3 I / A
6 (c) Complete the diagram below to show the circuit that could be used to obtain the data from which the graph was plotted. (3) (d) Use the graph, explaining your answers, to (i) determine the emf E of the cell; ........................................................................................................................... ........................................................................................................................... (2) (ii) determine the current in the external circuit when the resistance R of the external circuit is very small; ........................................................................................................................... ........................................................................................................................... ........................................................................................................................... ........................................................................................................................... (2)
7 (iii) deduce that the internal resistance r of the cell is about 1.2 Ω. ........................................................................................................................... ........................................................................................................................... ........................................................................................................................... ........................................................................................................................... (3) (e) The maximum power dissipated in the external circuit occurs when the resistance of the external circuit has the same value as the internal resistance of the cell. Calculate the maximum power dissipation in the external circuit. ..................................................................................................................................... ..................................................................................................................................... ..................................................................................................................................... ..................................................................................................................................... (3) 7. This question is about the possibility of generating electrical power using a satellite orbiting the Earth. (a) Define gravitational field strength. ..................................................................................................................................... ..................................................................................................................................... ..................................................................................................................................... (2) (b) Use the definition of gravitational field strength to deduce that GM = g0R 2 where M is the mass of the Earth, R its radius and g 0 is the gravitational field strength at the surface of the Earth. (You may assume that the Earth is a uniform sphere with its mass concentrated at its centre.) ..................................................................................................................................... ..................................................................................................................................... ..................................................................................................................................... ..................................................................................................................................... (2)
8 A space shuttle orbits the Earth and a small satellite is launched from the shuttle. The satellite carries a conducting cable connecting the satellite to the shuttle. When the satellite is a distance L from the shuttle, the cable is held straight by motors on the satellite. Diagram 1 Earth’s magnetic field satellite conducting cable L shuttle direction of orbit speed v EARTH As the shuttle orbits the Earth with speed v, the conducting cable is moving at right angles to the Earth’s magnetic field. The magnetic field vector B makes an angle θ to a line perpendicular to the conducting cable as shown in diagram 2. The velocity vector of the shuttle is directed out of the plane of the paper. Diagram 2 conducting cable B (c) On diagram 2, draw an arrow to show the direction of the magnetic force on an electron in the conducting cable. Label the arrow F. (1) (d) State an expression for the force F on the electron in terms of B, v, e and θ, where B is the
9 magnitude of the magnetic field strength and e is the electron charge. ..................................................................................................................................... (1) (e) Hence deduce an expression for the emf E induced in the conducting wire. ..................................................................................................................................... ..................................................................................................................................... ..................................................................................................................................... ..................................................................................................................................... ..................................................................................................................................... (3) (f) The shuttle is in an orbit that is 300 km above the surface of the Earth. Using the expression GM = g 0 R 2 and given that R = 6.4 × 10 6 m and g 0 = 10 N kg –1 , deduce that the orbital speed v of the satellite is 7.8 × 10 3 m s –1 . ..................................................................................................................................... ..................................................................................................................................... ..................................................................................................................................... ..................................................................................................................................... ..................................................................................................................................... ..................................................................................................................................... ..................................................................................................................................... (3)
10 (g) The magnitude of the magnetic field strength is 6.3 × 10 –6 T and the angle θ = 20°. Estimate the length L of the cable required in order to generate an emf of 1 kV. ..................................................................................................................................... ..................................................................................................................................... ..................................................................................................................................... (2) (Total 14 marks) 9. This question is about aspects of electric fields and electric charge. Fields and electric charge associated with atoms (a) Define electric field strength. ..................................................................................................................................... ..................................................................................................................................... (2) (b) A proton may be considered to be a point charge. For such a proton (i) sketch the electric field pattern.
· (2)
11 (ii) calculate the magnitude of the electric field strength at a distance of 5.0×10 –11 m from the proton. ........................................................................................................................... ........................................................................................................................... ........................................................................................................................... ........................................................................................................................... (2) (c) In a simple model of the hydrogen atom, an electron orbits the proton. Both electron and proton are regarded as point charges. The orbital radius of the electron is 5.0×10 –11 m. (i) Using your answer to (b)(ii) deduce that the magnitude of the electric force between the electron and the proton is 9.3×10 –8 N. ........................................................................................................................... (1) (ii) Deduce that the kinetic energy of the electron is 2.3×10 –18 J. ........................................................................................................................... ........................................................................................................................... ........................................................................................................................... ........................................................................................................................... ........................................................................................................................... (3) (iii) The total energy of the electron is –14 eV. Determine the potential energy of the electron in electron volt. ........................................................................................................................... ........................................................................................................................... ........................................................................................................................... ........................................................................................................................... ........................................................................................................................... (3) Fields and electric charge in conductors (d) Describe the concept of drift velocity as applied to the conduction electrons in a conductor.
12 ..................................................................................................................................... ..................................................................................................................................... ..................................................................................................................................... ..................................................................................................................................... ..................................................................................................................................... ..................................................................................................................................... (4)
13 (e) Define electromotive force (e.m.f.). ..................................................................................................................................... ..................................................................................................................................... (1) (f) A filament lamp is operating at normal brightness. The potential difference across the lamp is 6.0 V. The current in the filament is 0.20 A. For the filament of this lamp, calculate (i) the resistance. ........................................................................................................................... ........................................................................................................................... (1) (ii) the power dissipated. ........................................................................................................................... ........................................................................................................................... (1) (g) The lamp in (f) is connected in the circuit below. The lamp is still operating at normal brightness.
B R The battery B has an internal resistance of 5.0 W and the resistance R of the resistor is 15 W.
14 (i) Calculate the current in the resistor R. ........................................................................................................................... ........................................................................................................................... (1) (ii) Determine the e.m.f. of the battery. ........................................................................................................................... ........................................................................................................................... ........................................................................................................................... ........................................................................................................................... ........................................................................................................................... ........................................................................................................................... (4)
15 2. (a) (i) (ii) (b) (i) lines parallel and normal to plates; (ignore any edge effect) equally spaced; direction from (+) to (–); 3 curved path between plates and no curvature outside; in downward direction; 2 change = qDV; = 1.6 ×10 –19 × 750 = 1.2 × 10 –16 J; 2 Or 750 eV. ½mv 2 = 1.2 × 10 –16 ; ½ × 9.1 × 10 –31 × v 2 = 1.2 ×10 –16 / v 2 = 2.64 × 10 14 to give v = 1.67 × 10 7 m s –1 ; 2 inside solenoid, lines parallel to axis; line spacing about double at ends / lines equally spaced in solenoid; reasonable shape (symmetry and curving); correct direction (to left); 4 (ii) path with no deviation along axis; 1 (i) velocity component normal to field = 1.6 × 10 7 × sin 35; = 9.2 × 10 6 m s –1 ; 2 (ii) (c) (d) (i) (ii) circular motion; in plane normal to paper; ( 9 . 1 ´ 10 -31 ´ 9 . 2 ´ 10 6 ) mv 2 = Bqv / r = ; r ( 4 . 0 ´ 10 -3 ´ 1 . 6 ´ 10 -19 ) radius of circle = 1.3 × 10 –2 m; (e) 4 (iii) velocity component along field = 1.6 × 10 7 × cos 35 = 1.3 × 10 7 m s –1 ; 1 (iv) force is zero; because F = Bqv sinq and q = 0 or in “words”; 2 helical shape (allow spiral shape); any further detail eg constant pitch etc; 2 Award [2] for a good diagram. [25]
16 4. (a) (i)
® ¬; 1 general shape: at least one circle around each wire and one loop around both wires; appropriate spacing of lines: increasing separation with distance from wires; correct direction of field; 3 (ii) (b) velocity increases; acceleration increases; because the force is getting larger the closer the wires get together; 3 Watch for ecf if force is drawn in wrong direction in (a) (i) ie velocity increases, acceleration decreases, force gets smaller. 6. (a) (b) (i) EI; 1 (ii) I 2 r; 1 (iii) VI; 1 (from the conservation of energy), EI = I 2 r + VI; therefore, V = E – Ir / E = V + Ir; 2
17 (c) V A correct position of voltmeter; correct position of ammeter; correct position of variable resistor; (d) (i) (ii) (e) 3 E = V when I = 0; so E = 1.5 V; 2 recognize this is when V = 0; intercept on the x­axis = 1.3 (±0.1) A; 2 (iii) r is the slope of the graph; sensible choice of triangle, at least half the line as hypotenuse; 0 . 7 = ; 0 . 6 = 1.2 (±0.1)W or when V = 0 E = Ir; E r = I 1 . 5 = ; 1 . 3 = 1.2W 3 R = 1.2W; 1. 5 I = = 0.63A; 1 . 2 + 1 . 2 P = I 2 R = (0.63) 2 × 1.2 = 0.48W / 0.47 W; 3 [18] 8. (a) (b) force exerted per unit mass; on a small / point mass; from the law of gravitation, the field strength = g0 to give GM = g0R 2 ; 2 F
M = G 2 ; m R 2
18 NB To achieve full marks, candidates need to state that F = m g0. (c) downwards; (accept 90° to B field or down the wire) 1 (d) F = Bevcosθ; 1 (e) work done in moving an electron the length of the wire is W = FL = BevLcosθ; emf = work done per unit charge; therefore, E = BLvcosθ; or F electric field = = Bvcosθ; e emf E = electric field × L; to give E = BLvcosθ; 3 Award [2 max] if flux linkage argument is used.
19 (f) (g) Mm mv 2 = ; r r 2
GM g 0 R 2 such that v 2 = = ; r r 10 ´ ( 6 . 4 ) 2 ´ 10 12 v 2 = to give v = 7.8 × 10 3 m s –1 ; 6 . 7 ´ 10 6 F = G L =
= 10. (a) (b) E ; Bv cos q 10 3
- 6 3 6 . 3 ´ 10 ´ 7 . 8 ´ 10 ´ 0 . 93 =2.2 × 10 4 m; the force per unit charge; exerted on a small positive charge / positive test charge / positive point charge; 3 2 2 (i) at least 6 symmetric radial lines as shown touching the proton; correct direction; (ii) use of E = k 2 q r 2 9. 0 ´ 10 ´ 1 . 6 ´ 10 -13 9 E = ; 25 ´ 10 - 22 = 5.8 × 10 11 N C –1 ; Award full marks for bald correct answer.
2 20 (c) (i) (ii) use of F = qE F = 1.6 × 10 –19 × 5.8 × 10 11 ; = 9.3 × 10 –8 N Allow use of force law. recognize that F = mv 2 ; r 1 2 1 mv = Fr ; 2 2 1
= × 9.3 × 10 –8 × 5.0 × 10 –11 ; 2 = 2.3 × 10 –18 J (iii) kinetic energy = 2. 3 ´ 10 -18 1 . 6 ´ 10 -19 PE = Total – KE; = –28 (eV); (d) 1 3 = 14 eV; 3 (conduction) electrons have high random speeds; when accelerated by an electric field inside a conductor / OWTTE; although they collide (frequently) with lattice ions; they obtain a net speed in the direction opposite to the field direction; 4 (e) the power supplied per unit current / the energy supplied per unit charge; 1 (f) (i) æ 6 . 0 ö
R = ç
÷ = 30 W; è 0 . 2 ø
1 (ii) P = (6.0 × 0.2) = 1.2 W; 1 (i) æ 6 . 0 ö
I = ç
÷ = 0.40 A; è 15 ø
1
(g) 21 (ii) total current in the circuit 0.60 A; resistance of parallel circuit = 10Ω/ lost volts = 5.0 × 0.6; total resistance in circuit = 15Ω / lost volts = 3 V; e.m.f. = (0.60 × 15) = 9 V; or total current = 0.60 A; pd across R = 6.0 V; e.m.f. = 6.0 + 0.60 × 5.0; = 9.0 V; 4 [25]
22