Induced Voltage
Electricity and Magnetism
Level
3
\[\Large{x^{2}+y^{2} = t^{2}} \]
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.
by
Steven Chase