Induced Voltage

x24t2+y29t=1\large{\frac{x^{2}}{4t^{2}} + \frac{y^{2}}{9t}} = 1

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

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

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

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