Examstyle Questions: A Comparison of Electric and Gravitational Fields

The graphs in Fig. 1.1 show the variation with seperation r of (i) the electrostatic force F_{E} and (ii) the gravitational force F_{G} between two points.
a) State the relation between
i) F_{E} and r
ii) F_{G} and r.
(2 Marks)
b) Why is F_{E} positive, whereas F_{G} is negative?
(1 Mark)
c) The range of values or r represented by each graph is the same. State with a reason whether the F_{E} and F_{G} 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 10^{9} Nm^{2} C^{2} 4πε_{o} and Gravitational Field Constant = G = 6.7 x 10^{11} N m^{2} 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 outline and marking scheme for question:

a) i) F_{E} proportional to 1/r^{2} or F_{E} = Q^{2}/(4ðå _{0}r^{2}) or in words
ii) F_{G} proportional to () 1/r^{2} or F_{G} = () m^{2}G/r^{2}) or in words
(2 Marks)
b) Eletrostatic forces (between protons) always repulsive gravitational forces always attractive
(1 Mark)
c) (at equal seperations) magnitude of F_{E} >> magnitude of F_{G} so F_{E} scale has bigger range of values than F_{G}
(2 Marks)
(Marks available: 5)

a)
Electric field = 1 . Q (1 Mark) = 9.0 x 10^{9} x 1.6 x 10^{19} 4πε_{o} r^{2} (0.5 x 10^{10})^{2} = 5.76 x 10^{11} NC^{1}(1 Mark)
(2 Marks)
b) Electric Force = eE = 1.6 x 10^{19}x 5.76 x 10^{11} (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} r^{2} (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 10^{39} (1 Mark) Gravitational force 4.5 x 10^{47} (1 Mark)
(Marks available: 9)
(Maximum = 14 Marks)