The phenomenon of electro-magnetic induction is

Options

A. the process of charging a body
B. the process of generating magnetic field due to a current passing through a coil
C. producing induced current in a coil due to relative motion between a magnet and the coil
D. the process of rotating a coil of an electric motor

Explanation

**Step-by-Step Text Solution:**

1. **Understanding Electromagnetic Induction**: The phenomenon of electromagnetic induction refers to the generation of an electromotive force (emf) across a coil or conductor when there is a change in the magnetic field around it. This can occur due to the relative motion between a magnet and the coil.

2. **Magnetic Field Generation**: When an electric current passes through a coil, it generates a magnetic field around it. This is a fundamental principle of electromagnetism.

3. **Induced Current**: The key aspect of electromagnetic induction is that an induced current is produced in a coil when there is relative motion between the coil and a magnet. This means that either the magnet is moving towards or away from the coil, or the coil is moving in relation to a stationary magnet.

4. **Faraday's Law of Induction**: According to Faraday's law, the induced emf (E) in a coil is proportional to the rate of change of magnetic flux (Φ) through the coil. Mathematically, it is expressed as:
\[ E = -\frac{dΦ}{dt} \]
where \( \frac{dΦ}{dt} \) represents the change in magnetic flux over time.

5. **Resulting Induced Current**: As the magnetic flux changes due to the motion of the magnet or the coil, an emf is induced, which in turn causes an induced current to flow in the circuit connected to the coil.

6. **Conclusion**: Therefore, the phenomenon of electromagnetic induction is fundamentally about the generation of an induced current in a coil due to the relative motion between the coil and a magnetic field.

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