Induced Voltage

Electricity and Magnetism Level 3

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

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.