Dynamically induced EMF refers to the electromotive force (EMF) generated when a conductor moves through a magnetic field, thereby cutting the magnetic lines of force. This induces a voltage (or EMF) in the conductor, according to **Faraday's Law of Electromagnetic Induction**.
### Example of Dynamically Induced EMF:
**A Generator (Dynamo)**
A classic example of dynamically induced EMF is found in an **electric generator** (or dynamo). Here's how it works:
1. **Movement of Conductors**: In a generator, a coil or conductor rotates in a magnetic field. The movement is typically caused by mechanical energy (such as a spinning turbine driven by wind, water, steam, etc.).
2. **Cutting Magnetic Field Lines**: As the conductor moves within the magnetic field, it cuts through the magnetic lines of force. The relative motion between the magnetic field and the conductor induces an EMF in the conductor.
3. **Induced Voltage**: According to Faraday’s Law, the magnitude of the induced EMF depends on the rate of change of magnetic flux linkage. This means the faster the conductor moves through the magnetic field, the greater the induced EMF.
4. **Output**: The induced EMF is then used to produce electric current when the conductor is connected to a closed circuit.
#### Key Formula for Dynamically Induced EMF:
\[ e = B \cdot l \cdot v \]
Where:
- \(e\) = induced EMF (volts),
- \(B\) = magnetic flux density (Tesla),
- \(l\) = length of the conductor (meters),
- \(v\) = velocity of the conductor relative to the magnetic field (m/s).
### Real-World Example:
**Hydroelectric Power Plant Generator**: In a hydroelectric power plant, water flowing from a height turns a turbine, which rotates a generator. The rotating motion of the generator's rotor (which holds the conductors) within the magnetic field induces EMF, thereby generating electricity.
In summary, the electric generator is a prime example of dynamically induced EMF, where the mechanical motion of conductors in a magnetic field generates electrical energy.