An e.m.f. is produced in a coil, which is not connected to an external voltage source. This can be due to

Options

A. The coil being in a time varying magnetic field
B. The coil moving in a time varying magnetic field
C. The coil moving in a constant magnetic field
D. The coil is stationary in exteranl spatially magnetic field, which does not change with time

Explanation

To solve the question, we need to understand the phenomenon of electromagnetic induction and the conditions under which an electromotive force (e.m.f.) can be induced in a coil.

### Step-by-Step Solution:

1. **Understanding Electromagnetic Induction**:
- Electromagnetic induction occurs when a change in magnetic flux through a coil induces an e.m.f. in that coil. This is described by Faraday's law of electromagnetic induction.

2. **Identifying Conditions for Induced EMF**:
- For an e.m.f. to be induced in a coil, there must be a change in magnetic flux linked with the coil. This change can occur due to:
- **Movement of the coil in a magnetic field**: If the coil moves through a magnetic field, the amount of magnetic flux linked with the coil changes.
- **Change in the strength of the magnetic field**: If the strength of the magnetic field itself changes while the coil remains stationary, the magnetic flux linked with the coil will also change.
- **Change in the area of the coil**: If the area of the coil changes (for example, if the coil is stretched or compressed), the magnetic flux linked with the coil will change.

3. **Conclusion**:
- Therefore, the e.m.f. produced in a coil that is not connected to an external voltage source can be due to any of the following:
- Movement of the coil in a magnetic field.
- Change in the strength of the magnetic field.
- Change in the area of the coil.

### Final Answer:
The induced e.m.f. in a coil not connected to an external voltage source can be due to:
- Movement of the coil in a magnetic field.
- Change in the strength of the magnetic field.
- Change in the area of the coil.