The induced emf can be produced in a coil by
A. moving the coil with uniform speed inside uniform magnetic field
B. moving the coil with non uniform speed inside uniform magnetic field
C. rotating the coil inside the uniform magnetic field
D. changing the area of the coil inside the uniform magnetic field
Choose the correct answer from the options given below:

Options

A. B and C only
B. A and C only
C. C and D only
D. B and D only

Answer

To solve the problem of determining how induced electromotive force (emf) can be produced in a coil, we will analyze each option provided.

### Step 1: Understanding Induced EMF
Induced emf in a coil is produced due to a change in magnetic flux through the coil. According to Faraday's law of electromagnetic induction, the induced emf (ε) is given by the negative rate of change of magnetic flux (Φ) through the coil:
\[ \epsilon = -\frac{d\Phi}{dt} \]
Where magnetic flux (Φ) is defined as:
\[ \Phi = B \cdot A \cdot \cos(\theta) \]
Here, \(B\) is the magnetic field strength, \(A\) is the area of the coil, and \(\theta\) is the angle between the magnetic field and the normal to the surface of the coil.

### Step 2: Analyzing Each Option
**Option A: Moving the coil with uniform speed inside a uniform magnetic field**
- If the coil is moved with uniform speed in a uniform magnetic field, the magnetic flux through the coil does not change because both the magnetic field and the area of the coil remain constant. Thus, no induced emf is produced.
- **Conclusion**: This option does not produce induced emf.

**Option B: Moving the coil with non-uniform speed inside a uniform magnetic field**
- Moving the coil with non-uniform speed may change the rate at which the coil cuts through the magnetic field lines, but if the magnetic field and area remain constant, the overall magnetic flux may not change significantly. However, in practice, this could lead to some induced emf due to the varying speed.
- **Conclusion**: This option can produce induced emf, but it is less straightforward.

**Option C: Rotating the coil inside the uniform magnetic field**
- When the coil rotates in a uniform magnetic field, the angle \(\theta\) changes continuously, leading to a change in magnetic flux through the coil. This change in flux induces an emf according to Faraday's law.
- **Conclusion**: This option produces induced emf.

**Option D: Changing the area of the coil inside the uniform magnetic field**
- If the area of the coil changes while it is placed in a uniform magnetic field, the magnetic flux through the coil changes, resulting in induced emf.
- **Conclusion**: This option also produces induced emf.

### Final Answer
Based on the analysis:
- The correct options that can produce induced emf are **C (rotating the coil inside the uniform magnetic field)** and **D (changing the area of the coil inside the uniform magnetic field)**.

Thus, the correct answer is **C and D**.