Quick questions on Electromagnetic induction: flux, Faraday and Lenz: VCE Physics Unit 3

Magnetic flux through a flat loop of area $A$ in a uniform field $B$ is:

When the magnetic flux through a coil changes, an EMF is induced. For a coil of $N$ turns:

The direction of the induced current is such that the magnetic field it produces opposes the change in flux that produced it.

Bar magnet entering a coil. As the north pole approaches, flux into the coil increases; the induced current creates a field opposing the magnet (the near face of the coil becomes a north pole), repelling it.

As the north pole approaches, flux into the coil increases; the induced current creates a field opposing the magnet (the near face of the coil becomes a north pole), repelling it.

Flux decreases; the induced current reverses to maintain the original flux (the near face of the coil becomes a south pole), attracting the receding magnet.

$\Phi_B = BA \cos(\omega t)$. The EMF is $\varepsilon = NBA\omega \sin(\omega t)$, a sinusoidal AC waveform.

A bar of length $L$ moves with velocity $v$ on parallel rails through a field $B$ perpendicular to the loop. Area changes at rate $L v$, so $\varepsilon = B L v$.

A coil of 200 turns produces an EMF $200$ times that of a single loop.

$A$ is the area of one turn, not the total area of all turns added together. $N$ accounts for the turns separately.

$\Phi_B = B A \cos\theta$; if $B$ lies in the plane of the loop, $\Phi_B = 0$.

The induced current opposes the change in flux, not the flux itself. If flux is increasing into the page, the induced current creates flux out of the page. If flux is decreasing into the page, the induced current creates flux into the page (to maintain the original).

Lenz's law is what makes a generator hard to turn: the induced current creates a force that opposes the motion that produces the EMF. The mechanical energy input becomes electrical energy output.