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Questions on the field concept
A force field is a region in which a body experiences a non-contact force, and the three origins are mass, static charge, and moving charge. Field lines map the vector at every point, radial around a sphere and uniform close to a surface. Gravity and electrostatics are described in the same way, and differ in that gravity only attracts.
18 original questions · 45 marks · the field concept notes · Gravitational fields
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Define a force field.
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A region in which a body experiences a non-contact force (1); due to a property of the body such as its mass or charge (1).State the property of a body that gives rise to each of the following: a gravitational field, an electric field, a magnetic field.
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Gravitational field: mass; electric field: (static) charge (1); magnetic field: moving charge (or a permanent magnet) (1).A mass of 2.0 kg experiences a gravitational force of 19.6 N. Calculate the gravitational field strength at this point.
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g = F/m = 19.6/2.0 (1)
g = 9.8 N kg−1 (1)A diagram shows the gravitational field lines of a planet. State what is indicated by the direction of the arrow on a field line, and by the spacing of the lines.
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The arrow shows the direction of the (gravitational) force on a mass placed at that point (1); the spacing shows the strength of the field, with closer lines meaning a stronger field (1).Explain why two field lines can never cross.
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At a crossing point the field (force) would have two different directions at once (1); the force on a body at any point acts in only one direction, so lines cannot cross (1).A gravitational field is represented as a vector quantity. State the two pieces of information the field therefore carries at every point, and state how the direction of the field at a point is found.
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At every point the field carries both a strength (magnitude) and a direction (1); the direction is found by asking which way the force on a suitable test body placed at that point would act (1).Compare the gravitational force and the electric force between two point objects. State one similarity and two differences.
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Similarity: both obey an inverse-square law with separation (or both act at a distance) (1). Differences: gravitational force is always attractive whereas the electric force can be attractive or repulsive (1); the electric force between two charged particles is very much stronger than the gravitational force between them (1).A rock of mass 5.0 kg on the surface of a planet experiences a gravitational force of 40 N. Calculate the gravitational field strength at the surface of the planet.
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g = F/m = 40/5.0 (1)
g = 8.0 N kg−1 (1)Define gravitational field strength and state an appropriate unit for it.
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Force per unit mass on a small test mass placed at the point, g = F/m (1); unit: N kg−1 (or m s−2) (1).The table gives the gravitational field strength at the surface of three moons of a large planet.
moon P: 1.3 N kg−1
moon Q: 0.90 N kg−1
moon R: 2.2 N kg−1
A lander of mass 350 kg is damaged on touchdown if its weight exceeds 600 N. Deduce on which of the moons the lander can touch down safely.Mark scheme
Use of F = mg with each field strength (1)
P: 350 × 1.3 = 455 N; Q: 350 × 0.90 = 315 N; R: 350 × 2.2 = 770 N (1)
The lander is safe on P and Q; on R its weight exceeds 600 N (1).Explain why the Earth's gravitational field can be treated as uniform in a laboratory experiment, but must be treated as radial when analysing the motion of a distant satellite.
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Over laboratory distances the change in distance from the Earth's centre is negligible, so the magnitude of g is effectively constant (1); the field lines are effectively parallel and equally spaced, which is a uniform field (1). Over the distances travelled by a satellite, both the strength and the direction of the field change appreciably: the lines converge on the Earth's centre, so the field must be treated as radial (1).State what is meant by an equipotential surface, and state how much work is done when a mass moves along one.
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A surface joining points of equal potential: the contour line of the field (1); no work is done moving a mass along it (1).The gravitational field strength at the surface of Mars is 3.7 N kg−1. Calculate the gravitational force on a rover of mass 250 kg resting on the surface.
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F = mg = 250 × 3.7 (1)
F = 925 N (1)Describe the gravitational field line pattern around an isolated point mass, and the pattern in a uniform field close to the Earth's surface.
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Point mass: lines are radial (1); directed inwards towards the mass, with spacing increasing with distance as the field weakens (1). Near the Earth's surface: lines are parallel, vertical and directed downwards (1); equally spaced, showing the field strength is the same everywhere in the region (1).A space probe of mass 10 kg experiences a gravitational force of 82 N at a point above a planet. Calculate the gravitational field strength at that point and state the direction of the field.
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g = F/m = 82/10 (1)
g = 8.2 N kg−1 (1)
Directed towards the centre of the planet (1).Explain why gravitational forces are always attractive, whereas electric forces can be either attractive or repulsive.
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There is only one type of mass (1); masses always attract each other, so the gravitational force is always attractive (1). Charge exists in two types, positive and negative: like charges repel and unlike charges attract, so the electric force can act in either sense (1).A planet and its smaller moon are separated by a fixed distance. Explain why there is a point on the line joining their centres at which the resultant gravitational field strength is zero, and state, with a reason, whether this point lies closer to the planet or to the moon.
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Along the line, the two fields act in opposite directions: each points towards its own body (1). Moving from one body to the other, one field weakens while the other strengthens, so at some point their magnitudes are equal and the resultant is zero (1). The point is closer to the moon: the moon's smaller mass produces the weaker field, so the point of equality must lie nearer to it (1).Explain why the gravitational attraction between masses can never be cancelled or screened, and state the consequence for the large-scale structure of the universe.
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Charge exists in two signs, so electric attractions and repulsions can cancel each other; mass exists in one sign only (1). Every mass attracts every other, and with no negative mass there is nothing that can cancel or screen the attraction (1). The attraction therefore simply accumulates as mass gathers, which is what builds planets, stars and galaxies, the large-scale structure of the universe (1).
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