# Induced Voltage

$\large{\frac{x^{2}}{4t^{2}} + \frac{y^{2}}{9t}} = 1$

A conducting loop in the $$xy$$ plane takes the form of the curve given above. The parameter $$t$$ denotes time. Suppose that there is a uniform magnetic flux density $$B$$ which is normal to the $$xy$$ plane.

If the magnitude of the voltage induced in the loop at time $$t = 9$$ can be expressed as $$\alpha \pi B$$, determine the value of $$\alpha$$.

Details and Assumptions: Neglect units and assume that all physical expressions take their simplest forms.

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