Induced Voltage

\[\Large{x^{2}+y^{2} = t^{2}} \]

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 \(t = 2\) 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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