Fields and quantitative models in physics
Key ideas • General
Flashcards
Test your knowledge with interactive flashcards
Key concepts
What you'll likely be quizzed about
Definition of a field
A field is a region of space in which a physical quantity has a value at every point and can exert forces on objects. Fields remove the need for physical contact by describing how sources influence other objects through space. Limitations arise when fields are idealised; real sources often produce non-uniform fields and edge effects that require more detailed models.
Gravitational fields and weight
A gravitational field exerts an attractive force on any mass placed in it. Gravitational field strength, g, equals force per unit mass and usually has units N/kg. Weight, W, is the force on a mass m due to gravity and follows W = mg; doubling mass doubles weight because weight is directly proportional to mass. The model assumes constant g near a planet's surface; g varies with altitude and mass distribution, so W = mg is an approximation for near-surface conditions.
Electric fields and Coulomb's law
An electric field exerts forces on charged objects. Electric field strength, E, equals force per unit charge (E = F/q) and has units N/C. Coulomb's law gives the force between two point charges as F = k q1 q2 / r^2, so force is proportional to the product of charges and inversely proportional to the square of their separation. The point-charge model breaks down for extended charge distributions and at very small quantum scales.
Magnetic fields and magnetic effects
A magnetic field exerts forces on moving charges and magnetic materials. Field maps use lines that show direction and relative strength; closer lines indicate stronger fields. Forces on moving charges follow F = q v × B in vector form, and forces on current-carrying wires follow F = BIL for straight segments perpendicular to B. Magnetic field models assume steady currents and neglect relativistic corrections except at high speeds.
Proportionality and linear models (Hooke's law)
Proportionality describes a constant ratio between two quantities. Hooke's law states that the extension x of an elastic object is proportional to the force F applied, expressed as F = kx where k is the spring constant. The linear relationship holds only within the elastic limit; beyond that limit, permanent deformation or non-linear behaviour occurs and the model no longer applies.
Expressing physical laws in mathematical form
Physical laws become useful when written as equations that relate measurable quantities. Equations allow prediction, calculation and testing. Common examples include Newton's law of universal gravitation F = G m1 m2 / r^2, weight W = mg, and Hooke's law F = kx. Each equation includes variables, constants and specified conditions that indicate when the formula is valid.
Key notes
Important points to keep in mind