Faraday's law
Summary
Faraday's law says a changing magnetic flux through a loop of wire induces an emf equal to the number of turns times the rate of change of flux. The most testable point is that only a change in flux induces an emf. If the flux stays constant, there is no emf, no matter how strong the field.
Detail
Meaning: Magnetic flux is the field passing through a loop's area. An emf is induced whenever that flux changes: B changes, the area A changes, or the angle θ between B and the loop's normal changes (a generator coil). The minus sign is Lenz's law: the induced current opposes the change in flux.
Equation: ε = −N ΔΦ/Δt, with Φ = BA cosθ. ε: induced emf (V); N: turns (unitless); Φ: flux (Wb = T·m²); t: time (s); B: field (T); A: loop area (m²); θ: angle between B and the loop's normal (rad).
On the MCAT: Typical setups: a magnet pushed into a coil, a rod sliding on rails, a rotating loop. On a Φ–t graph the emf's magnitude is N times the slope (on a B–t graph, N·A·cosθ times the slope), and a flat segment means zero emf. Use I = ε/R for current and Lenz's law for direction.
Common confusion: Students think a strong field or large flux means a large emf. Only the rate of change of flux matters: a loop at rest in a strong, steady field has zero emf. So does a loop sliding within a uniform field.
Sources
- Physics (Giancoli)
- Fundamentals of Physics (Halliday, Resnick, Walker)
- University Physics (Young and Freedman)
Written for the MCAT and checked before it was published. For study reference only. Spotted an error? Let us know.