A coil of metal wire is kept stationary in a non-uniform magnetic field. An e.m.f. Is induced in the coil.

Options

A. An emf is is induced in the coil
B. A current is induced in the coil
C. Neither emf nor current is induced
D. Both (1) and (2)

Answer

To solve the problem of a coil of metal wire kept stationary in a non-uniform magnetic field and determining whether an electromotive force (e.m.f.) is induced, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding the Situation**:
- We have a coil of metal wire that is stationary.
- It is placed in a non-uniform magnetic field.

2. **Key Concepts**:
- According to Faraday's law of electromagnetic induction, an e.m.f. is induced in a coil when there is a change in magnetic flux through the coil.
- The magnetic flux (Φ) is defined as the product of the magnetic field (B) and the area (A) through which the field lines pass, considering the angle (θ) between the field lines and the normal to the surface:
\[ Φ = B \cdot A \cdot \cos(θ) \]

3. **Analyzing the Magnetic Field**:
- A non-uniform magnetic field means that the strength of the magnetic field (B) varies from one point to another.
- However, since the coil is stationary, the area (A) and orientation (θ) of the coil do not change.

4. **Determining Change in Flux**:
- Since the coil is stationary and there is no movement or rotation, there is no change in the area or orientation of the coil with respect to the magnetic field.
- Therefore, even though the magnetic field is non-uniform, there is no change in the magnetic flux through the coil.

5. **Conclusion**:
- Since there is no change in magnetic flux (ΔΦ = 0), according to Faraday's law, the induced e.m.f. (ε) is given by:
\[ ε = -\frac{dΦ}{dt} \]
- Since \(dΦ/dt = 0\), we conclude that:
\[ ε = 0 \]
- Thus, there is no induced e.m.f. or current in the coil.

### Final Answer:
- The correct conclusion is that neither e.m.f. nor current is induced in the coil.