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For a circular loop of radius r expanding at rate dr/dt in a uniform magnetic field B perpendicular to its plane:
$$\varepsilon = -\frac{d\Phi_B}{dt} = -B\,\frac{dA}{dt} = -B\,(2\pi r)\,\frac{dr}{dt}$$
where $$A = \pi r^2$$ and the negative sign indicates the induced EMF opposes the change in magnetic flux (Lenz's law).
