Gravitational vs electric fields 9702

The key differences between gravitational and electric fields lie in the nature of the source, the sign of the force, and the constants involved. Gravitational fields act on mass and are always attractive, while electric fields act on charge and can be either attractive or repulsive. According to expert tutors at My Physics Buddy, mastering this comparison is one of the highest-yield topics in A/AS Level Physics (9702).

Gravitational vs Electric Fields: A Complete Comparison for Cambridge 9702

These two field types are deliberately taught together in Cambridge 9702 because their mathematics is structurally identical — both follow an inverse-square law, both use the concept of field strength and potential, and both reward students who can move fluently between the two. As an IBDP Physics Facilitator and Head of Sciences with over 22 years of experience, I can tell you that the students who struggle most are those who try to memorise the differences as a list rather than understanding the underlying physics. Let’s fix that.

The Source of Each Field

Gravitational fields are created by any object with mass. Every particle of matter in the universe generates a gravitational field around it. There is no such thing as negative mass, so gravitational fields can only pull — they are always attractive.

Electric fields are created by objects with electric charge. Charge comes in two types — positive and negative — which means electric fields can both attract and repel. This is the single most important conceptual difference between the two field types.

The Force Laws: Newton and Coulomb Side by Side

Both forces follow an inverse-square law, meaning the force decreases with the square of the distance between the two objects. Compare the two laws directly:

Newton’s Law of Gravitation:

F = −GMm / r²

where G = gravitational constant (6.67 × 10⁻¹¹ N m² kg⁻²), M and m are the two masses in kg, and r is their separation in metres. The negative sign confirms the force is always attractive.

Coulomb’s Law:

F = kQ₁Q₂ / r²   or equivalently   F = Q₁Q₂ / (4πε₀r²)

where k = 8.99 × 10⁹ N m² C⁻², Q₁ and Q₂ are the charges in coulombs, ε₀ = 8.85 × 10⁻¹² F m⁻¹ is the permittivity of free space, and r is separation in metres. The sign of the force depends on the signs of the charges — like charges repel, unlike charges attract.

Field Strength

Gravitational field strength g is defined as the force per unit mass acting on a small test mass placed in the field:

g = F / m   (units: N kg⁻¹)

For a point mass or uniform sphere:   g = GM / r²

Electric field strength E is defined as the force per unit positive charge acting on a small positive test charge placed in the field:

E = F / Q   (units: N C⁻¹ or V m⁻¹)

For a point charge:   E = kQ / r²   or   E = Q / (4πε₀r²)

A helpful everyday analogy: think of gravitational field strength like water pressure at a certain depth — it tells you the force-per-unit-mass that would act on any object you drop in. Electric field strength is like wind speed — it tells you the force-per-unit-charge that would act on any charge you place there, but the direction of the push depends on whether the charge is positive or negative.

Potential

Gravitational potential φ at a point is the work done per unit mass in bringing a small test mass from infinity to that point:

φ = −GM / r   (units: J kg⁻¹)

Gravitational potential is always negative because you must do negative work against the attractive field — the field does positive work pulling mass inward.

Electric potential V at a point is the work done per unit positive charge in bringing a small positive test charge from infinity to that point:

V = kQ / r   or   V = Q / (4πε₀r)   (units: J C⁻¹ = V)

Electric potential can be positive (near a positive charge) or negative (near a negative charge).

Summary Comparison Table

Property	Gravitational Field	Electric Field
Source	Mass (always positive)	Charge (positive or negative)
Nature of force	Always attractive	Attractive or repulsive
Force law	F = GMm / r²	F = kQ₁Q₂ / r²
Field strength	g = GM / r² (N kg⁻¹)	E = kQ / r² (N C⁻¹)
Potential	φ = −GM / r (always ≤ 0)	V = kQ / r (can be + or −)
Constant	G = 6.67 × 10⁻¹¹ N m² kg⁻²	k = 8.99 × 10⁹ N m² C⁻²
Field lines	Always point inward (toward mass)	Away from + charge, toward − charge
Shielding	Cannot be shielded	Can be shielded (Faraday cage)
Relative magnitude	Extremely weak	Much stronger

Notice that the gravitational constant G is many orders of magnitude smaller than Coulomb’s constant k. This is why gravity, despite being the force that shapes galaxies, is actually the weakest of the fundamental forces at the particle scale — a point that surprises many students. You can explore the broader physics of these interactions further through Physics resources at My Physics Buddy, or check the official Cambridge syllabus notes at the Cambridge International A Level Physics 9702 page for the exact learning outcomes tested.

Uniform Fields

Both field types can also be uniform — that is, constant in both magnitude and direction across a region. For electric fields, a uniform field is produced between two large parallel charged plates. The field strength between the plates is:

E = V / d

where V is the potential difference across the plates in volts and d is the separation in metres. A gravitational uniform field approximation applies near Earth’s surface where g ≈ 9.81 N kg⁻¹ everywhere within a small region. Field lines in a uniform field are parallel and equally spaced — a key visual feature the examiners test directly.

Common Mistakes

✗ Mistake: Students write that gravitational potential can be positive, mirroring electric potential without checking the sign convention.
✓ Fix: Remember — gravitational potential is always zero at infinity and always negative at any finite distance, because gravity is always attractive. The formula φ = −GM/r has a permanent negative sign.

✗ Mistake: Students draw electric field lines pointing toward a positive charge, confusing the direction convention.
✓ Fix: Electric field lines always point in the direction of the force on a positive test charge — outward from a positive source charge, inward toward a negative source charge. Draw a small positive test charge and ask yourself: which way would it be pushed?

✗ Mistake: Students use the same formula structure but forget to swap the constants and quantities — mixing up G with k, or mass with charge — especially under exam pressure.
✓ Fix: Build a parallel two-column set of notes with gravitational on the left and electric on the right. Train yourself to always write both formulas together so the analogy becomes automatic, not accidental.

Exam Relevance: This comparison appears in Cambridge A/AS Level Physics 9702 (Units on Fields), Edexcel A Level Physics, and IB Physics HL/SL. Examiners frequently ask students to state similarities and differences or complete structured comparison tables directly.

Pro Tip from Jiya B: Always learn the gravitational and electric field equations as mirror pairs — whenever you write one, immediately write the other. This symmetry saves you in every comparison question.