D Fields

A field describes how a mass, a charge or a current changes the space around it, so that another mass, charge or current placed there feels a force without any contact. Theme D builds this one idea for gravity, for electric charge and for magnetism, then uses it to explain orbits, the motion of charged particles and the generation of electricity.

How the four subtopics fit together

D.1 Gravitational fields starts with Kepler’s laws of planetary motion and Newton’s law of gravitation, $F = Gm_1m_2/r^2$. It defines gravitational field strength as force per unit mass, pictures fields with field lines, and explains why satellites and planets move in orbits, with Kepler’s third law derived from the field.

D.2 Electric and magnetic fields applies the same model to charge. Coulomb’s law, $F = kq_1q_2/r^2$, has the same inverse-square form as Newton’s law, but charges can repel as well as attract. Electric field strength, field lines between plates and around charges, Millikan’s evidence that charge is quantised, and the magnetic field patterns of magnets, wires and solenoids all belong here.

D.3 Motion in electromagnetic fields asks what fields do to moving charges. A charge in a uniform electric field follows a parabola, like a projectile; a charge moving across a magnetic field follows a circle, like a satellite; and a current-carrying wire in a magnetic field feels a force, which is how electric motors work.

D.4 Induction (HL only) turns the last idea round. When the magnetic flux through a circuit changes, an emf is induced (Faraday’s law), in a direction that opposes the change (Lenz’s law). This is how the generators in power stations produce most of the world’s electricity.

Big ideas across the theme

One field model for several forces

Gravitational and electric fields are described with the same set of tools: a force law, a field strength (force per unit mass or per unit charge), field lines whose spacing shows strength, and, at HL, potential, potential energy and equipotential surfaces. Learning the model once for gravity makes the electric version faster to learn, and comparing the two shows what is different: gravity is always attractive and very weak, while electric forces can attract or repel and are enormously stronger.

Action at a distance and the field idea

Newton was uneasy that his law described a force acting across empty space. The field model answers this by giving each point in space a property, the field, that acts on whatever is placed there. In electromagnetism the field turned out to be physically real: a changing electric field produces a magnetic field and vice versa, and together they travel as light and other electromagnetic waves (C.2).

Energy in fields

Fields store energy. A satellite trades potential energy for kinetic energy as it moves in an elliptical orbit, an electron accelerated through a potential difference gains kinetic energy, and in D.4 mechanical work done against a magnetic force becomes electrical energy. Each is the conservation of energy from A.3, applied to a field.

Links to other themes

• Circular motion and Newton’s laws (A.2) explain orbits in D.1 and the circular paths of charges in D.3.

• Projectile motion (A.1) is the model for a charge moving through a uniform electric field.

• Current, potential difference and emf (B.5) are used throughout D.2 to D.4.

• Coulomb’s law explains alpha-particle scattering (E.1), and the balance between gravity and pressure keeps stars stable (E.5).

Standard level and higher level

At SL the theme concentrates on forces and field strengths: calculating forces between masses and charges, sketching field patterns, and predicting the motion of satellites and charged particles. At HL the same fields are also described by energy. Potential and equipotential surfaces map a field as contour lines map a landscape, and they make it possible to calculate how much energy a spacecraft needs to escape a planet or to change orbit, how much work moves a charge between two points, and, in D.4, how mechanical energy becomes electrical energy in a generator.