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 solve the problem, we need to analyze the two statements regarding the induction of electromotive force (emf).

### Step-by-Step Solution:

1. **Understanding Statement A**:
- The first statement claims that an emf can be induced by moving a conductor in a magnetic field.
- According to the principles of electromagnetic induction, when a conductor moves through a magnetic field, an emf is induced in the conductor. This is described by the formula:
\[ E = VBL \]
where \(E\) is the induced emf, \(V\) is the velocity of the conductor, \(B\) is the magnetic field strength, and \(L\) is the length of the conductor within the magnetic field.
- Since the motion of the conductor in the magnetic field results in the generation of emf, Statement A is **correct**.

2. **Understanding Statement B**:
- The second statement claims that an emf can be induced by changing the magnetic field.
- According to Faraday's law of electromagnetic induction, the induced emf in a circuit is proportional to the rate of change of magnetic flux through the circuit. The formula is given by:
\[ E = -\frac{d\Phi}{dt} \]
where \(\Phi\) is the magnetic flux, which can be expressed as \(\Phi = B \cdot A\) (where \(A\) is the area). If the magnetic field \(B\) changes over time, the induced emf can be calculated as:
\[ E = -A \frac{dB}{dt} \]
- Since the statement mentions that the magnetic field is changing, it confirms that an emf will indeed be induced. Therefore, Statement B is also **correct**.

3. **Conclusion**:
- Both statements A and B are true. Thus, the answer to the question is that both statements are correct.

### Final Answer:
Both statements A and B are true.

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