Electromagnetic Induction: the Sign Errors That Cost Marks

Treat the sign as physics, not bookkeeping

Lenz’s law says the induced effect opposes the change that caused it. That is a physical statement with a physical consequence, and it can be reasoned out in every question before any algebra happens: is the flux increasing or decreasing, and therefore which way must the induced current flow to resist that?

Students who answer that question first, in words, almost never get the direction wrong. Students who compute a magnitude and then try to attach a sign frequently do.

The sequence worth imposing

• Draw the field and mark its direction. Not optional — direction errors almost always begin with an unmarked diagram.
• State whether flux is increasing or decreasing. In words, on the page.
• Say what the induced current must oppose, and therefore its direction.
• Only then compute the magnitude. The sign is already settled by the reasoning above.

Where it recurs

Motional EMF, self and mutual inductance, and the whole of alternating current lean on this. A student shaky on induction direction will be shaky again in AC phase relationships, where the same reasoning appears in a different costume.

That is the argument for spending real time here rather than moving on once the formulae are memorised — the chapter is a prerequisite disguised as a chapter.

The practical questions

Rod-on-rails problems and rotating-coil problems are the standard board fare, and both are entirely tractable with the sequence above. The rotating coil in particular rewards a clear diagram at one instant rather than an attempt to reason about the whole rotation at once.

Questions parents ask