Induced Voltage

Electricity and Magnetism Level 4

\[\Large{\frac{x^{2}}{4t^{2}} + \frac{y^{2}}{9t}} = 1 \]

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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