Consider the following statements: (a)An emf can be induced by moving a conductor in a magnetic field. (b)An emf can be induced by changing the magnetic field.

Options

A. Both A and B are true
B. A is true but B is false
C. B is true but A is false
D. Both A and B are false

Answer

To analyze the given statements regarding electromagnetic induction, we will evaluate each statement step by step.

### Step 1: Evaluate Statement (a)
**Statement (a): An emf can be induced by moving a conductor in a magnetic field.**

1. **Understanding the Concept**: According to the principle of electromagnetic induction, when a conductor moves through a magnetic field, an electromotive force (emf) is induced across the ends of the conductor. This is known as motional emf.

2. **Mathematical Representation**: The induced emf (ε) can be calculated using the formula:
\[ \epsilon = B \cdot L \cdot v \]
where:
- \(B\) is the magnetic field strength,
- \(L\) is the length of the conductor,
- \(v\) is the velocity of the conductor relative to the magnetic field.

3. **Conclusion**: Since the statement mentions that an emf "can be induced," it is true. There are conditions under which this occurs, specifically when the conductor is moving perpendicularly to the magnetic field lines.

### Step 2: Evaluate Statement (b)
**Statement (b): An emf can be induced by changing the magnetic field.**

1. **Understanding the Concept**: According to Faraday's law of electromagnetic induction, a change in magnetic flux through a closed loop induces an emf in that loop. This can occur even if the conductor is stationary, as long as the magnetic field is changing.

2. **Mathematical Representation**: The induced emf (ε) due to a change in magnetic flux (Φ) is given by:
\[ \epsilon = -\frac{d\Phi}{dt} \]
where:
- \(\Phi\) is the magnetic flux, defined as \(B \cdot A\) (B is the magnetic field and A is the area through which the field lines pass).

3. **Conclusion**: Since the statement indicates that an emf "can be induced" by changing the magnetic field, it is also true. The change in the magnetic field leads to a change in magnetic flux, which induces an emf.

### Final Conclusion
Both statements (a) and (b) are true. Therefore, we conclude that:

- Statement (a) is true: An emf can be induced by moving a conductor in a magnetic field.
- Statement (b) is true: An emf can be induced by changing the magnetic field.

### Summary
Both statements are true as they align with the principles of electromagnetic induction.

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