Exam-style Questions: A Comparison of Electric and Gravitational Fields

  1. 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.

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    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)

  2. 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

    4πεo

    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:

  1. 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)

  2. a)

    Electric field = 1 . Q (1 Mark) = 9.0 x 109 x 1.6 x 10-19



    4πεo 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)