Electricity and magnetism

What the exam asks

Expect a diagram and one of three questions: which way does the force point, where is the field zero, or what path does the particle take. The formulae you need, F = k q1 q2 / r squared, E = V/d, F = qvB, F = BIL, are all supplied, so the marks sit in the geometry and the sign, not the algebra. The trap that catches most candidates is the negative charge: they get the field direction right, or the direction of v across B right, and then hand in the answer for a proton when the stem said electron. The second trap is treating a magnetic force as though it can speed a particle up. It cannot, ever, because it is always perpendicular to the motion, so a magnetic field bends a beam and leaves its speed alone. When a stem says a particle is held stationary or passes through undeflected, it has just told you two forces cancelled, and the answer it wants is an equation.

Two fields, and the forces they put on charges. An electric field acts on any charge, moving or not, along the direction of the field. A magnetic field acts only on charges that are moving, only on the part of their motion that crosses the field, and always at right angles to both. Nearly everything in this topic follows from those two sentences.

The exam works the topic through diagrams: field lines between charges, a charge between parallel plates, a wire in a field, a particle fired into a region marked with dots or crosses. The formulae are printed in the stem. What you carry in is the geometry, which way the force points, and the sign.

Equilibrium items are the most common of the lot. A charge sits still between two others, a drop hangs between charged plates, a beam crosses a region and comes out undeflected. Each of those is a sentence saying two forces cancelled, and turning it into an equals sign is the whole question.

What to hold

• An electric field line shows the direction of the force on a positive test charge, and how tightly the lines are packed shows the field's strength. Two lines can never cross, because the field at a point has exactly one direction.
• Electric field lines begin on positive charge and end on negative charge, and they meet the surface of a conductor at right angles.
• A negative charge feels a force opposite to the field it sits in. The field's direction is fixed by the charges that made it and does not flip because the charge you put there is negative.
• Coulomb's law is an inverse square: double the separation and the force falls to a quarter. The two charges always feel the same size of force, in opposite directions, however unequal they are.
• Between parallel plates the field is uniform and equal to V/d, so a charge in it feels the same force wherever it is in the gap.
• On the line between two like charges there is a point where the field is zero, and it lies nearer the weaker charge. Between two unlike charges there is no such point, because both contributions point the same way and add.
• A magnetic field exerts no force on a stationary charge, and none on a charge moving parallel to the field.
• The magnetic force is perpendicular to both the velocity and the field, so it does no work. It changes a particle's direction and never its speed.
• A charge fired perpendicular into a uniform magnetic field travels in a circle, because a force of constant size that stays at right angles to the velocity is exactly what centripetal means.
• Magnetic field lines form closed loops with no beginning and no end, because there are no magnetic monopoles for them to start or stop on.
• Around a long straight current-carrying wire the field is a set of circles centred on the wire, weakening with distance from it.
• Two parallel wires carrying current the same way attract, and carrying it opposite ways repel. This is the reverse of how two like charges behave, and the analogy with charge is a trap rather than a help.