ANS:C - both (a) and (b).

In magnetic flow meters, voltage generation is proportional to the fluid velocity. Here's an explanation: Magnetic flow meters, also known as electromagnetic flow meters, operate on the principle of Faraday's Law of Electromagnetic Induction. According to this principle, a voltage is induced across a conductor (in this case, the conductive fluid) when it moves through a magnetic field. The magnitude of the induced voltage (or electromotive force, EMF) is directly proportional to the velocity of the fluid and the strength of the magnetic field.

• Motion of Conducting Fluid through an Externally Generated Uniform Field: This describes the setup of a magnetic flow meter, where a magnetic field is applied externally and uniformly across the flow path. The conducting fluid (typically a liquid with ions or charged particles) passes through this magnetic field.
• Proportional to the Fluid Velocity: The induced voltage VVV across the electrodes in the magnetic flow meter is directly proportional to the average velocity vvv of the fluid: V∝vV \propto vV∝v This relationship holds true as long as the magnetic field strength remains constant and the flow profile is sufficiently uniform.

Therefore, in magnetic flow meters, the voltage generation (or EMF generation) is primarily due to the fluid velocity moving through the externally generated magnetic field. Hence, the correct answer is: proportional to the fluid velocity In a magnetic flow meter, the principle of operation relies on Faraday's Law of Electromagnetic Induction. Here’s a detailed explanation of why the voltage generated in a magnetic flow meter is proportional to the fluid velocity:

1. Faraday's Law of Electromagnetic Induction: According to Faraday's Law, whenever a conductor (such as a conductive fluid) moves through a magnetic field, an electromotive force (EMF) or voltage VVV is induced across the conductor. The magnitude of this induced voltage is directly proportional to the rate of change of magnetic flux linkage with respect to time.
2. Application in Magnetic Flow Meters: In a magnetic flow meter:
   • A magnetic field is generated externally and uniformly across the flow path of the conductive fluid.
   • The conductive fluid flows through this magnetic field, cutting through the magnetic lines of flux.
   • As the fluid moves, the magnetic flux through the fluid changes, which induces a voltage VVV across electrodes placed in contact with the fluid.
3. Proportional Relationship: The induced voltage VVV is proportional to the average velocity vvv of the fluid: V∝vV \propto vV∝v This means that as the fluid velocity vvv increases, the induced voltage VVV also increases proportionally. Conversely, if the fluid velocity decreases, the induced voltage VVV decreases accordingly.
4. Factors Affecting Proportionality: The proportionality between induced voltage VVV and fluid velocity vvv assumes a constant magnetic field strength and a uniform flow profile. Real-world factors such as flow disturbances, variations in fluid conductivity, and non-uniform flow profiles can affect the accuracy of this proportionality, but under ideal conditions, it holds true.
5. Measurement Principle: By measuring the induced voltage VVV, the magnetic flow meter can calculate the fluid velocity vvv. Since the induced voltage VVV is directly proportional to vvv, the flow meter can provide an accurate measurement of flow rate based on this relationship.

In summary, the voltage generated in a magnetic flow meter is proportional to the fluid velocity because of the fundamental principle of electromagnetic induction (Faraday's Law). This proportionality forms the basis for accurate flow rate measurement in applications where conductivity of the fluid allows for the use of electromagnetic principles.