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What is the working principle of moving coil galvanometer?

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A moving coil galvanometer is an instrument used to measure small electric currents. Its working principle is based on the interaction between a magnetic field and a current-carrying coil. Here’s how it works:

1. **Structure**: The galvanometer consists of a coil of wire (the moving coil) suspended in a uniform magnetic field, typically produced by permanent magnets. The coil is mounted on a pivot, allowing it to rotate.

2. **Current Flow**: When an electric current passes through the coil, it generates a magnetic field around it due to Ampère's law. The direction of the magnetic field created by the coil depends on the direction of the current.

3. **Magnetic Interaction**: The coil's magnetic field interacts with the external magnetic field from the magnets. This interaction creates a torque on the coil, causing it to rotate. The direction of the rotation depends on the direction of the current.

4. **Deflection and Scale**: As the coil rotates, it moves a pointer attached to it across a graduated scale. The angle of deflection of the pointer is proportional to the strength of the current passing through the coil.

5. **Restoring Torque**: A spring or a similar mechanism provides a restoring torque that opposes the rotation of the coil. The system reaches equilibrium when the torque due to the current is balanced by the restoring torque, allowing for a stable reading on the scale.

6. **Calibration**: The galvanometer is calibrated so that specific deflections correspond to known currents, allowing for accurate measurements.

In summary, a moving coil galvanometer measures current by utilizing the torque generated by the interaction of magnetic fields, translating this mechanical movement into an electrical measurement.
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The **moving coil galvanometer** works on the principle that when a current-carrying coil is placed in a magnetic field, it experiences a torque, causing the coil to rotate. The deflection of the coil is directly proportional to the current passing through it, allowing the galvanometer to measure small currents.

### Working Principle:
1. **Current Flow**: When a small current flows through the coil of the galvanometer, it generates a magnetic field around the coil.
  
2. **Magnetic Field Interaction**: The coil is suspended between the poles of a permanent magnet, which has a strong radial magnetic field. The interaction between the magnetic field generated by the current in the coil and the radial magnetic field of the permanent magnet creates a torque.

3. **Torque and Deflection**: This torque causes the coil to rotate. The rotation is proportional to the amount of current flowing through the coil. The coil is attached to a pointer that moves over a calibrated scale, showing the deflection.

4. **Restoring Force**: The coil is attached to a spring (or some fine suspension), which provides a restoring torque. This spring opposes the rotation of the coil. When the magnetic torque (due to the current) is balanced by the restoring torque (from the spring), the coil reaches a stable position.

5. **Proportional Deflection**: The deflection (θ) of the pointer is proportional to the current (I) flowing through the coil, i.e.,  
   \[ \theta \propto I \]

### Key Components:
- **Coil**: A rectangular coil wound on a light frame that rotates when current flows through it.
- **Magnet**: A strong permanent magnet provides the radial magnetic field. Horseshoe magnets are often used.
- **Soft Iron Core**: Positioned inside the coil to make the magnetic field radial, ensuring uniform sensitivity.
- **Suspension and Spring**: The coil is suspended using fine springs, which also conduct the current into and out of the coil and provide the restoring torque.

### Applications:
- **Measurement of Small Currents**: It is used to detect and measure very small electric currents in circuits.
- **Basis of Ammeter/Voltmeter**: By modifying the moving coil galvanometer (adding resistances), it can be converted into an ammeter or a voltmeter.

### Summary:
In essence, a moving coil galvanometer converts an electric current into mechanical deflection through the interaction of a current-carrying coil and a magnetic field. The resulting deflection is proportional to the magnitude of the current, making it a sensitive instrument for detecting and measuring small currents.
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