Answer:
A) The circular one
Explanation:
When there is a loop of wire in a magnetic field, and the magnetic flux through the coil changes, an electromotive force is induced in the coil, according to Faraday-Newmann-Lenz law:
![\epsilon = - \frac{ N\Delta \Phi}{\Delta t}](https://tex.z-dn.net/?f=%5Cepsilon%20%3D%20-%20%5Cfrac%7B%20N%5CDelta%20%5CPhi%7D%7B%5CDelta%20t%7D)
where
N is the number of turns in the coil
is the change in magnetic flux through the coil
is the time interval
The variation of flux through a coil can be written as
![\Delta \Phi =A \Delta B](https://tex.z-dn.net/?f=%5CDelta%20%5CPhi%20%3DA%20%5CDelta%20B)
where
A is the area of the coil
is the change in magnetic field
Here we have three loops of wire: one circular, one rectangular, one square.
The length of the wire used for the 3 loops is the same, therefore their perimeter is also the same.
The change in magnetic flux is directly proportional to the area enclosed by the loop: therefore, the loop that will experience the greatest induced emf is the one having the greatest area.
Since the circle is the 2D figure that maximizes the area for a given perimeter, this means that the circular loop has the greatest area, and so also the greatest induced emf.