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 a contant velocity `vec(v)=vhati` . The magnetic field is directed along the negative `z`-axis direction. The induced emf, during the passege of these loops , out of the field region, will not remain constant for

Options

A. the rectangular, circular and elliptical loops
B. the circular and the elliptical loops
C. only the elliptical loop
D. any of the four loops

Explanation

To solve the problem, we need to analyze the induced electromotive force (emf) in each of the given loops (rectangular, square, circular, and elliptical) as they move out of a uniform magnetic field. The magnetic field is directed along the negative z-axis, and the loops are moving with a constant velocity in the x-direction.

### Step-by-Step Solution:

1. **Understanding the Setup**:
- We have four types of loops: rectangular, square, circular, and elliptical.
- All loops are in the x-y plane and are moving out of a uniform magnetic field directed along the negative z-axis.

2. **Induced EMF Formula**:
- The induced emf (\( \mathcal{E} \)) in a loop can be calculated using Faraday's law of electromagnetic induction, which states:
\[ \mathcal{E} = -\frac{d\Phi_B}{dt} \]
- Here, \( \Phi_B \) is the magnetic flux through the loop, given by:
\[ \Phi_B = B \cdot A \]
- Where \( B \) is the magnetic field strength and \( A \) is the area of the loop within the magnetic field.

3. **Analyzing Each Loop**:
- **Rectangular Loop**:
- As the rectangular loop moves out of the magnetic field, a constant width (breadth) of the loop is exiting the field at a constant velocity. The area exiting per unit time remains constant.
- Thus, the induced emf will remain constant.

- **Square Loop**:
- Similar to the rectangular loop, the square loop has a constant width and length. As it exits the magnetic field, the area change per unit time is constant.
- Therefore, the induced emf will also remain constant.

- **Circular Loop**:
- For the circular loop, as it exits the magnetic field, the area that exits is not uniform. The edge of the circle that is exiting changes as the loop moves, leading to a varying area exiting the field.
- Hence, the induced emf will not remain constant.

- **Elliptical Loop**:
- The elliptical loop behaves similarly to the circular loop. As it moves out of the magnetic field, the area that exits changes non-uniformly due to the shape of the ellipse.
- Thus, the induced emf will also not remain constant.

4. **Conclusion**:
- The induced emf will remain constant for the rectangular and square loops but will not remain constant for the circular and elliptical loops.
- Therefore, the answer to the question is that the induced emf will not remain constant for the **circular and elliptical loops**.

### Final Answer:
The induced emf will not remain constant for the circular and elliptical loops.