In this problem, we'll apply Faraday's law to determine the magnitude of the induced emf and Lenz's law to determine the direction.

Induced emf:

$\overline{){\mathbf{\epsilon}}{\mathbf{=}}{\mathbf{N}}\frac{\mathbf{\u2206}\mathbf{\varphi}}{\mathbf{\u2206}\mathbf{t}}}$, where Φ is the magnetic flux, N is the number of turns, t is the time, and A is the cross-sectional area of the coil.

Lenz's law: The induced current flows in a direction such that it opposes the change in flux inducing it.

Power rule of derivation:

$\overline{)\frac{\mathit{d}}{\mathit{d}\mathit{t}}\mathbf{\left(}{\mathit{x}}^{\mathit{n}}\mathbf{\right)}{\mathbf{=}}{\mathit{n}}{{\mathit{x}}}^{\mathit{n}\mathbf{-}\mathbf{1}}}$

The magnetic flux through the loop shown in the figure below increases according to the relation Φ_{B} =6.0*t*^{2} + 6.4*t*, where Φ_{B} is in milliwebers and *t* is in seconds.

(a) What is the magnitude of the emf induced in the loop when *t* = 2.9 s?

mV

(b) What is the direction of the current through *R*?

left

right

insufficient information

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