A rectangular, a square, a circular and an elliptical loop, all in the(x-y) plane, are moving out of a uniform magnetic field with aconstant velocity 𝑣⃗ = v𝚤̂.The magnetic field is directed along thenegative z-axis direction. The induced emf, during the passage ofthese loops, out of the field region, will not remain constant for(i) any of the four loops(ii) the circular and elliptical loops(iii) the rectangular, circular and elliptical loops(iv) only the elliptical loops1

The induced emf (electromotive force) in a loop due to a changing magnetic field is given by Faraday's law of electromagnetic induction, which states that the induced emf is equal to the rate of change of magnetic flux through the loop.

The magnetic flux through a loop is given by the product of the magnetic field strength, the area of the loop, and the cosine of the angle between the magnetic field direction and the normal to the loop. In this case, since the loops are in the (x-y) plane and the magnetic field is along the negative z-axis, the angle is 90 degrees and the cosine of the angle is 0. Therefore, the magnetic flux is zero and there is no induced emf.

However, as the loops move out of the magnetic field region, the area of the loop that is within the magnetic field changes, and so does the magnetic flux through the loop. This change in magnetic flux induces an emf in the loop.

For a rectangular or square loop, the rate of change of the area within the magnetic field, and hence the rate of change of magnetic flux, is constant as the loop moves out of the field region with a constant velocity. Therefore, the induced emf remains constant.

For a circular or elliptical loop, the rate of change of the area within the magnetic field is not constant as the loop moves out of the field region. This is because the shape of the area within the field changes as the loop moves out. Therefore, the induced emf does not remain constant.

So, the induced emf will not remain constant for the circular and elliptical loops. Therefore, the correct answer is (ii) the circular and elliptical loops.