Moving Charges and Magnetism: Getting the Direction Right Every Time

Pick one hand and stay with it

Students arrive having been shown a right-hand rule at school, a left-hand rule in a reference book and a corkscrew rule by a friend. Each works. Used together, in the same paper, they produce a student who is confident and wrong.

The version that generalises best is the vector one: the force on a moving charge is the cross product of its velocity with the magnetic field, scaled by the charge. Point the fingers along the velocity, curl them towards the field, and the thumb gives the direction for a positive charge. Then the step almost everyone forgets: if the charge is negative, reverse it. In our experience that single omission accounts for more lost direction marks than anything else in the chapter.

Two laws, and knowing which one is allowed

Students reach for whichever law they remember rather than the one the situation permits, so it is worth making the distinction explicit.

• Biot–Savart. General. It works for any current element, but it commits you to an integral, which is why it is used for the standard geometries and not in a hurry.
• Ampere’s circuital law. A shortcut, and only available where the symmetry is good enough to make the line integral trivial — a long straight wire, a long solenoid, a toroid.

Where there is no such symmetry, Ampere’s law is still true but useless, because the integral cannot be evaluated without already knowing the answer. A student who understands that sentence stops misapplying it.

The results worth having cold

A small set of standard results covers most of what is asked: the field near a long straight wire, the field at the centre of a circular loop, the field on the axis of a loop, and the field inside a long solenoid. These should be recallable without derivation, and derivable when the question asks for a derivation.

Two further items are reliably examined and reliably muddled. The force between two parallel currents attracts when the currents run in the same direction, and students guess this every year; derived once from the two rules already established, it stops being a guess. And the motion of a charged particle in a uniform magnetic field gives a circle whose radius depends on the speed but whose time period does not — the fact on which the whole cyclotron question rests.

The easiest marks in the chapter

Converting a galvanometer into an ammeter or a voltmeter is short, numerically simple, and asked often. A low resistance is placed in parallel as a shunt to make an ammeter; a high resistance goes in series to make a voltmeter. Students who cannot picture what each instrument is for tend to swap them. The check that settles it: an ammeter goes into the circuit and must not disturb the current, so it needs a very low resistance; a voltmeter sits across a component and must not divert the current, so it needs a very high one.

One more line is worth writing on the first page of the chapter. A magnetic force does no work on a moving charge, because the force is always perpendicular to the velocity. Students can state this and still write energy solutions that quietly assume otherwise.

Fitting a Class 12 slot in Delhi

We teach at home across Delhi, Noida and Gurgaon, and online anywhere. In Delhi a Class 12 physics slot has to survive the whole board year, so it should be realistic in January and not merely comfortable in July. Ask at the start how far the tutor is travelling and what happens to the slot during pre-boards. For a chapter that is mostly drawing and correcting diagrams, a live online session is genuinely equivalent, and often more punctual.

Questions parents ask