OCR Specification focus:
‘Compare and contrast point-charge electric fields with point-mass gravitational fields.’
Electric and gravitational fields share deep conceptual similarities, yet their origins, strengths, and effects differ significantly. Understanding these parallels and distinctions strengthens conceptual mastery and supports skilled problem-solving across field situations.
Comparing Electric and Gravitational Fields
Electric and gravitational fields are both central force fields that extend through space and influence objects without physical contact. The specification requires students to compare and contrast point-charge electric fields with point-mass gravitational fields, focusing on their source, mathematical form, vector behaviour, and physical implications.
Key Similarities
Both fields are governed by inverse-square laws, meaning their magnitudes decrease proportionally to the square of the distance from the source. This shared mathematical structure produces similar field shapes and directional properties. Because they are both radial fields, they act along lines directly connecting interacting bodies.
As distance increases, field lines spread over a sphere whose surface area grows as 4πr², causing field strength to fall according to an inverse-square relationship. Source.
Both act at a distance without contact.
Both originate from a point source: a point charge for electric fields and a point mass for gravitational fields.
Both exert forces proportional to properties of interacting objects (charge or mass).
Both create field lines that radiate symmetrically in three dimensions.
Both follow superposition principles, meaning total field at a point is the vector sum of contributions from all sources.
Despite these parallels, the fields differ profoundly in how they interact with matter and the strengths of the forces involved.
Fundamental Differences
Electric fields arise from electric charge, whereas gravitational fields arise from mass. Electric charges can be positive or negative, but mass is always positive, which leads to a key behavioural distinction: gravitational forces are always attractive, while electric forces may be attractive or repulsive.
Because the electrical interaction is far stronger than gravity, electric forces dominate at atomic and everyday laboratory scales, while gravity dominates at astronomical scales.
Electric vs Gravitational Force Laws
Both force laws share the same structural form, but their constants and variables differ.
EQUATION
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Coulomb’s Law (F) = (1 / (4πɛ₀)) · (Qq / r²)
F = Electric force between two point charges, newton (N)
Q = Charge of first object, coulomb (C)
q = Charge of second object, coulomb (C)
r = Separation of charges, metre (m)
ɛ₀ = Permittivity of free space, farad per metre (F m⁻¹)
—-----------------------------------------------------------------
Between two masses, the gravitational equivalent takes a similar form. This structural similarity explains why field diagrams and directional behaviour match so closely. However, the constants produce drastically different magnitudes.
EQUATION
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Newton’s Law of Gravitation (F) = G · (Mm / r²)
F = Gravitational force between two point masses, newton (N)
M = Mass of first object, kilogram (kg)
m = Mass of second object, kilogram (kg)
r = Separation of masses, metre (m)
G = Gravitational constant, N m² kg⁻²
—-----------------------------------------------------------------
These expressions illustrate that gravitational forces are immensely weaker. Even small net electric charges generate far stronger forces than large masses.
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Electric Field Strength vs Gravitational Field Strength
Field strength describes the force experienced per unit property of an object placed in the field. In electric fields, that property is charge, and in gravitational fields, it is mass.
Electric Field Strength: Force per unit positive charge at a point in an electric field.
Gravitational Field Strength: Force per unit mass at a point in a gravitational field.
Although their definitions mirror each other, their physical sources differ, leading to important consequences for motion.
Direction and Behaviour of Field Lines
Field lines show the direction a test object would move under the field’s influence.
Electric field lines radiate outward from positive charges and inward toward negative charges, illustrating direction and radial symmetry. The density of lines indicates relative field strength. Source.
Electric field lines:
Radiate outward from positive charges.
Converge inward toward negative charges.
May indicate attraction or repulsion depending on charge signs.
Gravitational field lines:
Always point towards the mass creating the field.
Never diverge outwards because gravity cannot be repulsive.
Gravitational field lines show a uniform inward radial pattern, emphasising that gravity is always attractive. Line density increases near the mass, representing stronger gravitational influence. Source.
Because of this asymmetry, gravitational systems exhibit stable large-scale structures (planets, stars, galaxies), whereas electric systems often neutralise quickly due to charge attraction.
Energy Considerations
Although not treated mathematically in this subsubtopic, comparing the fields conceptually requires recognising how potential energy behaves in each field type.
Opposite charges brought closer decrease electric potential energy.
Like charges brought closer increase electric potential energy.
Two masses brought closer always decrease gravitational potential energy, because gravitational interactions are always attractive.
This difference reflects the contrasting directions of force.
Influence on Matter
Electric forces are many orders of magnitude stronger, allowing electric fields to significantly alter the motion of small charged particles. Gravitational effects dominate only when extremely large masses are involved.
Key contrasting influences:
Electric fields strongly affect electrons, ions, and other charged particles.
Gravitational fields are negligible for atomic-scale objects but crucial for celestial mechanics.
Neutral objects experience no electric force but always experience gravitational force.
Summary of Core Contrasts in Line with the Specification
To meet the OCR requirement, the following distinctions should be clearly understood:
Electric fields arise from charge; gravitational fields arise from mass.
Electric forces may attract or repel; gravitational forces attract only.
Both fields obey inverse-square laws, yet electric forces are enormously stronger.
Field line structures mirror their force behaviours, diverging or converging according to the sign of charge or direction of mass-based attraction.
FAQ
Both fields arise from central forces that depend only on distance from a point source. Whenever a force spreads out uniformly through three-dimensional space, its strength falls with the surface area of a sphere, which increases with the square of the radius.
The physical origins differ, but the underlying geometry of three-dimensional space forces both interactions to adopt an inverse-square form.
A positive test charge moves in the direction of the electric field, while a negative test charge moves opposite to the field direction. This produces a wide range of possible motions.
In contrast, any mass always accelerates towards the source mass, giving gravitational motion greater predictability and fewer possible trajectories.
Mass exists only as positive quantities, so the force between masses is always attractive.
Electric charge exists in two types, positive and negative.
Like charges repel.
Unlike charges attract.
The presence of two charge signs allows electric fields to show both behaviours.
Gravitational interactions dominate when objects are electrically neutral overall, which is typical for astronomical systems. Any small residual charges rapidly neutralise, eliminating electric effects.
Large masses such as planets and stars produce significant gravitational fields, while the net electric field across such bodies remains essentially zero.
Both fields obey superposition mathematically, but in real systems electric superposition often involves cancelling effects because charges can have opposite signs. This can create regions where electric field strength is reduced or zero.
Gravitational superposition always adds contributions from masses, since all masses attract. As a result, gravitational fields accumulate rather than cancel, giving more uniform large-scale behaviour.
Practice Questions
Question 1 (2 marks)
Explain one similarity and one difference between the electric field around a point charge and the gravitational field around a point mass.
Mark scheme:
Award 1 mark for any valid similarity and 1 mark for any valid difference.
Similarities (max 1 mark):
Both are radial fields acting at a distance.
Both follow inverse-square laws.
Both exert forces proportional to properties of the test object (charge or mass).
Differences (max 1 mark):
Electric fields can be attractive or repulsive, gravitational fields are always attractive.
Electric fields arise from charge, gravitational fields arise from mass.
Electric forces are much stronger than gravitational forces.
Question 2 (5 marks)
A student claims that electric and gravitational fields behave in the same way because both follow inverse-square laws.
Discuss this claim. In your answer, you should refer to:
• the vector nature and direction of each field
• the possible types of force produced
• the properties of the sources that create each field
• the relative strengths of the two interactions.
Mark scheme:
Award marks for the following points (maximum 5):
Both fields follow an inverse-square law, giving similar radial field shapes. (1 mark)
Electric fields can produce attraction or repulsion depending on charge sign; gravitational fields only attract. (1 mark)
Electric fields originate from electric charge; gravitational fields originate from mass. (1 mark)
Direction of electric field lines depends on charge sign, while gravitational field lines always point towards the mass. (1 mark)
Electric forces are far stronger than gravitational forces for typical laboratory-scale objects. (1 mark)
Alternative valid points should be credited where appropriate.
