The fictitious generator

From the circuit’s point of view, the quantity $-d\Phi_B/dt$ behaves exactly like an electromotive force (EMF): a genuine generator, albeit a virtual one, that drives the charges around the loop.

Induced EMF

$\ev{\text{EMF}_\text{ind} = -\frac{d\Phi_B}{dt}}$

If the circuit has resistance $R$, the induced current is obtained from Ohm’s law just as for an ordinary battery:

$i = \frac{|\text{EMF}|}{R} = \frac{1}{R}\left|\frac{d\Phi_B}{dt}\right|$

The idea of the “fictitious generator” is a powerful pedagogical fiction: once $\text{EMF}_\text{ind}$ is inserted in the right place, all of Kirchhoff’s equations work identically to circuits with real batteries. There is no physical cell in the loop, and yet the charges move as if there were one: the source is the change in the linked magnetic flux.

Links

Topics: Electromagnetic induction Concepts: Faraday-Neumann-Lenz law · Electromotive force Skills: Flux balance

Related exercises: EMF on a moving rod · s) · Alternator: from peak EMF to angular frequency