Field Forces

A field force is a force that acts between two objects without any physical contact between them. Unlike contact forces such as friction or a normal force — which require objects to touch — field forces are transmitted through regions of space called fields. The three fundamental field forces encountered in high school physics are gravitational force, electric force, and magnetic force. Each field permeates space around its source object, and a second object placed in that field experiences a force whose magnitude and direction depend on the field's strength at that location. The concept of a field was one of the most profound shifts in scientific thinking. Rather than asking 'how does the Sun pull Earth across empty space?' physicists introduced the idea that the Sun creates a gravitational field throughout space, and Earth responds to the field at its own location. This two-step picture — source creates field, field exerts force on test object — removes the philosophical puzzle of 'action at a distance' and provides a framework that extends naturally into modern physics, including electromagnetism and general relativity. At the high school level, field forces are treated through three iconic force laws: Newton's Law of Universal Gravitation for gravity, Coulomb's Law for electric forces, and the Lorentz force law for magnetic interactions. Understanding these laws quantitatively allows students to calculate forces between planets, predict the deflection of charged particles, and explain the operation of electric motors — all without any object touching another.

Key takeaways
  • What Is a Field?
  • Gravitational Force
  • Electric Force (Coulomb's Law)
  • Magnetic Force
  • Comparing the Three Field Forces

What Is a Field?

A field is a physical quantity that has a value at every point in space. A gravitational field g at a point in space is defined as the gravitational force per unit mass that a small test mass would experience there: g = F/m. Similarly, an electric field E at a point is the electric force per unit positive charge: E = F/q. Fields are vector quantities — they have both magnitude and direction at every location. The source of the field (e.g., a planet or a charged sphere) sets up the field; any other object with the relevant property (mass or charge) then experiences a force F = mg or F = qE at its location.

Gravitational Force

Every object with mass attracts every other object with mass via gravity. Newton's Law of Universal Gravitation states that the magnitude of the gravitational force between two point masses m₁ and m₂ separated by distance r is F = Gm₁m₂/r², where G = 6.674 × 10⁻¹¹ N·m²/kg² is the universal gravitational constant. The force is always attractive and acts along the line joining the two masses. Near Earth's surface, the gravitational field strength is approximately g = 9.8 N/kg (or 9.8 m/s²), so the gravitational force on an object of mass m is simply F_g = mg directed downward toward Earth's centre.

Electric Force (Coulomb's Law)

Charged objects exert electric forces on each other without contact. Coulomb's Law gives the magnitude of the electric force between two point charges q₁ and q₂ separated by distance r: F_E = k|q₁||q₂|/r², where k = 8.99 × 10⁹ N·m²/C² is Coulomb's constant (also written as k = 1/(4πε₀), with ε₀ = 8.85 × 10⁻¹² C²/(N·m²) the permittivity of free space). Like charges repel; opposite charges attract. The electric force is approximately 10³⁶ times stronger than gravity for two protons — electric forces dominate atomic and molecular physics, while gravity dominates on astronomical scales where matter is electrically neutral.

Magnetic Force

A magnetic field B exerts a force on a moving charged particle but not on a stationary one. The magnetic force on a particle of charge q moving with velocity v in a magnetic field B is given by the Lorentz force: F_B = qv × B. The magnitude is F_B = |q|vB sinθ, where θ is the angle between the velocity vector and the magnetic field vector. The direction is perpendicular to both v and B, determined by the right-hand rule. Because the magnetic force is always perpendicular to the velocity, it does no work on the particle and changes only the direction of motion, not the speed. Magnetic forces are responsible for the circular motion of charged particles in cyclotrons and the deflection of cosmic rays by Earth's magnetic field.

Comparing the Three Field Forces

All three field forces share the key property of action at a distance mediated by a field, and all obey Newton's Third Law — the force on object A due to object B is equal in magnitude and opposite in direction to the force on B due to A. However, they differ importantly: gravity is always attractive and acts on any mass; electric forces can be attractive or repulsive and act only on charged objects; magnetic forces act only on moving charges and are always perpendicular to motion. In terms of strength at the atomic scale: strong nuclear > electromagnetic > weak nuclear > gravitational, though only electromagnetic forces (electric and magnetic) and gravity are relevant at the high school level.

The Key Equation

F=Gm1m2r2F = \frac{Gm_1 m_2}{r^2}
  • F — Gravitational force (Newton (N)): The magnitude of the attractive force each mass exerts on the other; direction is along the line joining the centres, attractive.
  • G — Universal gravitational constant (N·m²/kg²): G = 6.674 × 10⁻¹¹ N·m²/kg²; an extremely small number reflecting the weakness of gravity compared with other fundamental forces.
  • m_1,\, m_2 — Masses of the two objects (kilogram (kg)): The inertial (and gravitational) masses of the two interacting objects. Doubling either mass doubles the force.
  • r — Separation distance (metre (m)): The centre-to-centre distance between the two objects. Gravity follows an inverse-square law: doubling r reduces F by a factor of 4.

Worked Example

Problem. The International Space Station (ISS) orbits at an altitude of 4.00 × 10⁵ m above Earth's surface. Earth's mass is M_E = 5.97 × 10²⁴ kg, Earth's radius is R_E = 6.37 × 10⁶ m, and G = 6.674 × 10⁻¹¹ N·m²/kg². (a) Calculate the gravitational field strength g at the ISS's orbital altitude. (b) If the ISS has mass m = 4.20 × 10⁵ kg, calculate the gravitational force on it.

g≈8.69 N/kg;F=mg≈3.65×106 Ng \approx 8.69\text{ N/kg};\quad F = mg \approx 3.65 \times 10^6\text{ N}

Answer. The gravitational field strength at the ISS altitude is approximately 8.69 N/kg, and the gravitational force on the ISS is approximately 3.65 × 10⁶ N.

Figure
Diagram
EarthM = 5.97×10²⁴ kgISSm = 4.20×10⁵ kgr = 6.77×10⁶ mF_g = 3.65×10⁶ NGravitational Field Force(non-contact force across empty space)Field lines (not shown) point radially inward toward Earth's centre
Origins · 1 minMichael Faraday and how this was discovered
MF
Michael Faraday
1791–1867 · British

Michael Faraday introduced the modern concept of the field in physics. Dissatisfied with 'action at a distance,' he proposed that electric and magnetic forces are transmitted through continuous 'lines of force' permeating space — the precursor to what we now call electric and magnetic fields. His experiments on electromagnetic induction (Faraday's Law) showed that a changing magnetic field produces an electric field, a discovery that underpins generators and transformers. James Clerk Maxwell later gave Faraday's intuitive field concept a precise mathematical form, leading to Maxwell's equations and the prediction of electromagnetic waves. Faraday had almost no formal mathematical training — he taught himself science by reading books while working as a bookbinder's apprentice. Despite this, he became one of the most influential experimental scientists in history, and Einstein kept a portrait of Faraday on his study wall alongside those of Newton and Maxwell.

  • Force as Interaction — Field forces are a specific class of force; understanding force as an interaction between two objects is the foundation needed before distinguishing contact forces from field forces.
  • Balanced vs Unbalanced Forces — Field forces such as gravity contribute to the net force on an object; analysing whether field forces are balanced or unbalanced determines whether an object accelerates.
  • Law of Inertia — An object subject only to a gravitational field force (free fall) still obeys Newton's First Law in its own free-fall frame; connecting field forces to inertia deepens understanding.
  • Mass as Measure of Inertia — Mass appears in both Newton's Law of Universal Gravitation (gravitational mass) and F = ma (inertial mass); their equality is a deep principle exploited in all field-force calculations.
  • F = ma Formulation — Once a field force is calculated (e.g., F_g = GMm/r²), Newton's Second Law F = ma is used to find the resulting acceleration, linking force laws to kinematics.
  • Identifying Net Force — Field forces (gravity, electric) often act simultaneously with contact forces; correctly identifying and summing all forces including field forces is essential for applying Newton's Second Law.
  • Action–Reaction Principle — Field forces obey Newton's Third Law: Earth pulls the ISS with 3.65 × 10⁶ N and the ISS pulls Earth with an equal and opposite force. This is a key consequence of field forces being interactions.
  • Identifying Interaction Pairs — With field forces it can be tempting to forget the reaction force (e.g., the Moon pulling Earth). Identifying interaction pairs correctly is especially important when field forces act over large distances.