The graphs in Fig. 1.1 show the variation with seperation r of (i) the electrostatic force FE and (ii) the gravitational force FG between two points. a) State the relation between i) FE and r ii) FG and r. (2 Marks) b) Why is FE positive, whereas FG is negative? (1 Mark) c) The range of values or r represented by each graph is the same. State with a reason whether the FE and FG scales cover the same range of values. (2 Marks) (Marks available: 5) A hydrogen atom appears to behave like a proton orbited by an electron with an orbit radius of 0.50 x 10-10 m. Given that - ekectronic charge = 1.6 x 10-19 C. electron mass = 9.1 x 10-31 kg proton mass = 1.7 x 10-27 kg Electric field constant = 1 = 9.0 x 109 Nm2 C-2 4πε o and Gravitational Field Constant = G = 6.7 x 10-11 N m2 kg-2 Calculate: a) the electric fild at a distance of 0.5 x 10-10 m from a proton. (2 Marks) b) the electrical force on an electron at that distance from a proton. (2 Marks) c) the Gravitational Field at a distance of 0.5 x 10-10 m from a proton. (2 Marks) d) the gravitational force on an electron at that distance from a proton. (2 Marks) e) the ratio of the electrical force to the gravitational force on an electron. (1 Mark) (Marks available: 9) Answer Answer outline and marking scheme for question: a) i) FE proportional to 1/r2 or FE = Q2/(4ðå 0r2) or in words ii) FG proportional to (-) 1/r2 or FG = (-) m2G/r2) or in words (2 Marks) b) Eletrostatic forces (between protons) always repulsive gravitational forces always attractive (1 Mark) c) (at equal seperations) magnitude of FE >> magnitude of FG so FE scale has bigger range of values than FG (2 Marks) (Marks available: 5) a) Electric field = 1 . Q (1 Mark) = 9.0 x 109 x 1.6 x 10-19 4πε o r2 (0.5 x 10-10)2 = 5.76 x 1011 NC-1(1 Mark) (2 Marks) b) Electric Force = eE = 1.6 x 10-19x 5.76 x 1011 (1 Mark) = 9.22 x 10-8 N (1 Mark) (2 Marks) c) Gravitational field = GM = 6.7 x 10-11 x 1.7 x 10-27 r2 (0.5 x 10-10)2 = 4.56 x 10-17 N kg-1 (1 Mark) (2 Marks) d) Gravitational force = mass x gravitational field = 9.1 x 10-27 x 4.56 x 10-17 (1 Mark) = 4.15 x 10-47 N (1 Mark) (2 Marks) e) Electrical force = 9.22 x 10-8 = 2.2 x 1039 (1 Mark) Gravitational force 4.5 x 10-47 (1 Mark) (Marks available: 9) (Maximum = 14 Marks)