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:

For a single conducting loop, the induced EMF around the loop equals the negative rate of change of flux:

The induced EMF and induced current always act in a direction that opposes the change in flux that produced them.

A conducting rod of length $L$ moving with velocity $v$ perpendicular to a uniform field $B$ (with $L$, $v$ and $B$ mutually perpendicular) has free charges in it experiencing a magnetic force $q v B$ along the rod. Charges separate until an electric field inside the rod balances the magnetic force. The resulting EMF between the ends of the rod is:

A 100-turn rectangular coil of area $0.020$ m$^2$ rotates at $50$ Hz in a uniform field of $0.10$ T.

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.

A 100-turn coil with a flux change of 1 Wb produces 100 times more EMF than a single loop with the same change.

The minus sign encodes Lenz's law. For magnitude questions, work with $|\varepsilon|$; a separate sentence then explains direction using Lenz's law.

A large steady flux produces zero EMF. Only a changing flux does.

It opposes the change in flux, not the field itself. If the external field is decreasing, the induced current reinforces it (its induced field points the same way as the external field).

They are the same law; motional EMF is what Faraday's law gives when the area changes in a steady field.

Mechanical power input = electrical power dissipated. If the two do not match, recheck signs and the Lenz's-law direction of the magnetic force on the rod.