Induced emf produced in a coil rotating in a magnetic field will be maximum when the angle between the axis of coil and direction of magnetic field is

Options

A. `0^(@)`
B. `90^(@)`
C. `45^(@)`
D. `180^(@)`

Explanation

To determine the angle at which the induced electromotive force (emf) produced in a coil rotating in a magnetic field is maximum, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding Induced EMF**: The induced emf (ε) in a coil rotating in a magnetic field is given by Faraday's law of electromagnetic induction. The formula for induced emf can be expressed as:
\[ \epsilon = -\frac{d\Phi}{dt} \]
where \(\Phi\) is the magnetic flux through the coil.

2. **Magnetic Flux Expression**: The magnetic flux (\(\Phi\)) through the coil 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 direction and the normal (perpendicular) to the surface of the coil.

3. **Change in Magnetic Flux**: As the coil rotates, the angle \(\theta\) changes, leading to a change in magnetic flux. The induced emf can also be expressed as:
\[ \epsilon = -\frac{d}{dt}(B \cdot A \cdot \cos(\theta)) \]

4. **Maximizing Induced EMF**: To maximize the induced emf, we need to maximize the rate of change of magnetic flux. The cosine function reaches its maximum value of 1 when \(\theta = 0^\circ\). This means that the area vector of the coil is aligned with the magnetic field.

5. **Conclusion**: Therefore, the induced emf produced in a coil rotating in a magnetic field will be maximum when the angle between the axis of the coil and the direction of the magnetic field is:
\[ \theta = 0^\circ \]

### Final Answer:
The angle between the axis of the coil and the direction of the magnetic field for maximum induced emf is \(0^\circ\).

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