Questions on Fields
1. (a) (i) Cp = 2 + 4 = 6 μF A1
(ii) 1/C = 1/2 + ¼ C1
Cs = 4/3 =1.33 μF A1
(b) (i) 6.0 V A1
(ii) Q = CpV C1
= 6 × 6 = 36 μC A1
(c) E = ½ CsV2 C1
= 24 × 10–6 A1
(d) (i) The capacitors discharge through the voltmeter. B1
(ii) V = V0e–t/CR
1/4 =e–t/(6×12) C1
ln 4 = t / 72 C1
t = 72 ln 4 ≈ 100 s A1
[12]
2. It is the force (of attraction) per unit mass. B1
[1]
3. (i) Suitable recognisable pattern around (not just between) the charges B1
Quality mark: symmetry, spacing, lines joined to charges B1
Consistent arrows toward B on some lines B1
(ii) Use of E = (1/4πε0)Q/r2 C1
Sum of two equal terms
E = 2 × 9 × 109 × 1.6 × 10–19 / (2.0 × 10–10)2 C1
E = 7.2 × 1010 N C–1 or V m–1 A1
(iii) The separation between the ions because this has an effect on the
breaking force. (Allow the size of ionic ‘charges’) B1
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4. (i) The gravitational field strength g is not constant. B1
The student’s value would be greater than the actual value (because the
average magnitude of g is less than 9.81 m s–1). B1
(ii) KE = 1/2 mv2
v = 2πr / T C1
v = 2 × π × (6800 + 6400) × 103 / 8.5 × 103 / v = 9.76 × 103 (m s–1) C1
KE = 1/2 × 1500 × (9.76 × 103)2
KE = 7.1(4) × 1010 (J) A1
(iii) A geostationary satellite stays above the same point on the Earth and as B1
such can be used for radio communications. (the term communications to M1
be included and spelled correctly to gain the mark). A1
The satellite is not in geostationary orbit
because its period is less than 1 day / 8.6 × 104 s.
[8]
5. (a) forces FS and FG acting inwards, force FE acting outwards - all through
centre of proton;
3 forces 2/2, 2 forces 1/2, marked and labelled (2) 2
(b) FE = FS + FG;
accept FE + FS + FG = 0 allow ecf from (a) (1) 1
(c) (i) FE = Q2 / (4π ε0 r2) (1)
= (1.6 × 10–19)2 / [4π × 8.85 × 10–12 (2.8 × 10–15)2] = 29 N (1)
use of r = 1.4 × 10–15 m (–1) once only 2
(ii) FG = m2 G / r2 (1)
= (1.67 × 10–27)2 × 6.67 × 10–11 / (2.8 × 10–15)2 = 2.4 × 10–35 N (1) 2
(iii) FS = 29 N / same as FE allow ecf (1) 1
(d) FE >> FG so FG negligible / insignificant / can be ignored or AW (1) 1
(e) (i) FE = 0 (1) 1
(ii) FG = 2.4 × 10–35 N (approx.) allow ecf (1) 1
(iii) FS = 2.4 × 10–35 N (approx.) (1)
comment: FS now repulsive (not attractive) or AW
or indicated by minus sign with FS; (1) any 3 1
[12]
6. (i) r has been increased by a factor of 3 from the centre of planet. C1
g = (40/32 =) 4.4(4) (N kg–1) A1
(ii) M = gr2 / G
M = (40 × [2.0 × 107]2) / 6.67 × 10–11 C1
M = 2.4 × 1026 (kg) A1
(iii) M = ρV = 4/3 πr3 ρ M1
g = GM / r2 r3 / r2 (Hence g r) A1
[6]
7. The astronaut is accelerating / has centripetal acceleration (1)
and the space station has the same acceleration (1)
a person does not feel gravity (1)
only feels forces applied by contact with the walls of the space station (1)
no support force from the space station (as they have the same acceleration) (1) 4
MAXIMUM (4)
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