Quick questions on Electromagnetic induction, Faraday's law and Lenz's law (QCE Physics Unit 3)

The magnetic flux through a flat coil of area $A$ in a uniform field $\vec{B}$ at angle $\theta$ to the area normal:

Expect a coil-in-changing-field setup with a flux-vs-time graph and questions on the EMF in each segment, or a moving-rod-on-rails diagram with motional EMF and the direction of the induced current. Markers focus on candidates who drop the $N$ factor, or who state that the induced current opposes "the field" rather than "the change in flux".

Common IA2 designs include: a bar magnet dropped through a coil (with peak EMF measured against drop height); a coil rotated at variable frequency between magnets (peak EMF vs frequency); a sliding rod on rails through a fixed magnet (EMF vs speed). Strong reports linearise $\varepsilon$ against the variable (e.g. $\varepsilon$ vs $v$ for the sliding rod) and report a slope consistent with $B L$ within uncertainty.

State Faraday's law of electromagnetic induction. [2 marks]

A $50$-turn coil of area $0.04 \text{ m}^2$ in a field changing from $0.30 \text{ T}$ to $0.10 \text{ T}$ in $0.20 \text{ s}$. Calculate the induced EMF magnitude. [3 marks]

A Bundaberg generator coil ($N = 200$, $A = 0.25 \text{ m}^2$) rotates at $50 \text{ Hz}$ in $B = 1.2 \text{ T}$. (a) Calculate the peak EMF. (b) Apply Lenz's law to identify the direction of the induced current as flux through the coil increases.