Revise Electric and magnetic fields for IB Physics (D.2)

Electric charge is a fundamental property of matter that comes in two kinds, positive and negative, and is measured in coulombs (C). The rule is simple and worth stating out loud before every problem: like charges repel and unlike charges attract. Charge is quantised — it always comes in whole-number multiples of the elementary charge $e = 1.60 \times 10^{-19}$ C — and it is conserved: it can be moved around but never created or destroyed.

The force between two point charges is given by Coulomb's law. It is an inverse-square law: double the separation and the force falls to a quarter; treble it and the force falls to a ninth. The force acts along the straight line joining the two charges.

$F = k\,\frac{q_1 q_2}{r^2}, \qquad k = \frac{1}{4\pi\varepsilon_0} \approx 8.99 \times 10^9 \ \text{N m}^2\,\text{C}^{-2}$

Here $q_1$ and $q_2$ are the two charges, $r$ is their separation, and $\varepsilon_0 = 8.85 \times 10^{-12}$ C² N⁻¹ m⁻² is the permittivity of free space. In practice, compute the magnitude of the force from the sizes of the charges, then decide attractive or repulsive from their signs. Treating the sign as part of the arithmetic is where marks are lost.

Rather than talk about the force between two specific charges, we describe the influence of a single charge on the space around it using the electric field. The electric field strength $E$ at a point is defined as the force per unit charge that a small positive test charge would feel there.

$E = \frac{F}{q}, \qquad \text{and for a point charge } Q: \quad E = k\,\frac{Q}{r^2}$

The single most common conceptual error in this topic is getting the field direction wrong near a negative charge. The field is defined by the force on a positive test charge, so near a negative charge the field points toward the charge (the positive test charge is attracted), regardless of what a negative test charge would do.

Field lines are a picture of the field. Their direction at any point is the direction of the force on a positive test charge, and their spacing shows the strength — lines packed close together mean a strong field. Electric field lines always start on positive charge and end on negative charge, and they never cross (if they did, the field would point in two directions at once).

The parallel-plate case is especially important because the field there is uniform: the same magnitude and direction everywhere between the plates. Its strength is set by the potential difference $V$ across the plates and their separation $d$:

$E = \frac{V}{d} \qquad (\text{uniform field between parallel plates})$

A magnetic field is a region where a moving charge, a current, or another magnet feels a magnetic force. Magnetic field lines run from north to south OUTSIDE a magnet, always forming closed loops — there are no isolated magnetic poles for a line to start or end on, which is a key structural difference from electric fields. As always, lines drawn closer together mean a stronger field, so the field is strongest at a magnet's poles.

The right-hand rule is the tool that ties current direction to field direction. Remember that conventional current flows from the positive terminal to the negative terminal — the opposite direction to the flow of electrons — so always apply the rule to the conventional current, not to the electron drift.

Bringing the three fields together sharpens what each one is. A gravitational field acts on any mass and is only ever attractive; the field of a point mass obeys an inverse-square law. An electric field acts on charge, can be attractive or repulsive, and the field of a point charge also obeys an inverse-square law — the parallel between $F = k q_1 q_2 / r^2$ and Newton's $F = G m_1 m_2 / r^2$ is exact in form. A magnetic field is the odd one out: it acts only on moving charges, currents and magnets, and its field lines always form closed loops.

The following ideas are HL only. The electric potential $V$ at a point is the work done per unit positive charge in bringing a small test charge from infinity to that point. For a point charge it is $V = kQ/r$, measured in volts (J C⁻¹). Notice it falls off as $1/r$, one power gentler than the field, which falls as $1/r^2$. Unlike the field, potential is a scalar, so contributions from several charges simply add as numbers.

$V = k\,\frac{Q}{r} \qquad\text{and}\qquad E_p = k\,\frac{q_1 q_2}{r} \qquad (\text{HL only})$

The electric potential energy of a pair of point charges is $E_p = k q_1 q_2 / r$ — the work done to assemble them from infinity. It is positive for like charges (you must do work to push them together) and negative for unlike charges (they pull themselves together). SL students can safely skip this section; HL students should be able to move between potential, potential energy and field with confidence.

In Paper 2 the marks are analytic: each is tied to a specific line of working — a method mark (M) or an answer mark (A) — and error-carried-forward (ECF) means a wrong number early on does not have to cost you the marks that follow. But that protection only exists if your method is written down. Study how each mark below is earned by a specific line, especially the separation of the magnitude (from the sizes of the charges) from the direction (from their signs).

Fields are the thread that runs through the rest of D. The inverse-square electric field here is the direct partner of the gravitational field, and the parallel-plate result $E = V/d$ reappears whenever charges are accelerated, from cathode-ray tubes to particle accelerators. The magnetic field patterns you have drawn become the stage on which moving charges feel the magnetic force $F = qvB$, and the right-hand rule carries straight into electromagnetic induction. HL students will build electric potential into a full energy picture that mirrors gravitational potential. Master the habit — identify the source, draw the field, put a number on it with the right equation, and read direction from signs and the right-hand rule — and the fields that follow become variations on a method you already own.