An emf can be induced in stationary coil if it is kept in

Options

A. Stationary uniform magnetic field
B. Stationary nonuniform magnetic field
C. Time varying magnetic field
D. Not possible

Answer

To solve the question "An emf can be induced in a stationary coil if it is kept in...", we will follow these steps:

### Step 1: Understand the Concept of Electromagnetic Induction
Electromagnetic induction refers to the process by which a changing magnetic field can induce an electromotive force (emf) in a coil or conductor. According to Faraday's law of electromagnetic induction, the induced emf in a coil is directly related to the rate of change of magnetic flux through the coil.

### Step 2: Define Magnetic Flux
Magnetic flux (Φ) through a coil is defined as:
\[ \Phi = B \cdot A \cdot \cos(\theta) \]
where:
- \(B\) is the magnetic field strength,
- \(A\) is the area of the coil,
- \(\theta\) is the angle between the magnetic field lines and the normal to the surface of the coil.

### Step 3: Analyze the Situation
In this case, the coil is stationary, which means that:
- The area \(A\) of the coil remains constant.
- The angle \(\theta\) between the magnetic field and the normal to the coil surface is also constant.

### Step 4: Apply Faraday's Law
According to Faraday's law, the induced emf (E) in the coil is given by:
\[ E = -\frac{d\Phi}{dt} \]
Substituting the expression for magnetic flux:
\[ E = -\frac{d}{dt}(B \cdot A \cdot \cos(\theta)) \]
Since \(A\) and \(\cos(\theta)\) are constant, we can simplify this to:
\[ E = -A \cdot \cos(\theta) \cdot \frac{dB}{dt} \]

### Step 5: Determine Conditions for Induced EMF
For the induced emf \(E\) to be non-zero, the term \(\frac{dB}{dt}\) must not be zero. This means that the magnetic field \(B\) must be changing with time.

### Step 6: Conclusion
Thus, an emf can be induced in a stationary coil if it is kept in a region where the magnetic field is varying with time. Therefore, the correct answer is that an emf can be induced in a stationary coil if it is kept in a time-varying magnetic field.

### Final Answer
An emf can be induced in a stationary coil if it is kept in a time-varying magnetic field.

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