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Divergence in Spherical & Cylindrical Coordinate -2 Video Lecture | Crash Course for IIT JAM Physics

FAQs on Divergence in Spherical & Cylindrical Coordinate -2 Video Lecture - Crash Course for IIT JAM Physics

1. What is divergence in spherical coordinates?

Ans. Divergence in spherical coordinates is a mathematical concept used to measure the rate at which a vector field spreads out or converges at a particular point in space. It is represented by the symbol ∇ · F, where ∇ is the del operator and F is the vector field.

2. How is divergence calculated in cylindrical coordinates?

Ans. In cylindrical coordinates, divergence is calculated using the following formula: ∇ · F = (1/ρ) ∂(ρF_ρ)/∂ρ + (1/ρ) ∂F_φ/∂φ + ∂F_z/∂z, where ρ is the radial distance, φ is the azimuthal angle, and z is the vertical coordinate.

3. What does a positive divergence indicate in spherical coordinates?

Ans. A positive divergence in spherical coordinates indicates that the vector field is spreading out from the point of interest. This means that the vector field has a source at that point, and the magnitude of the field is increasing as we move away from it.

4. Can divergence be negative in cylindrical coordinates?

Ans. Yes, divergence can be negative in cylindrical coordinates. A negative divergence indicates that the vector field is converging towards the point of interest. This means that the vector field has a sink at that point, and the magnitude of the field is decreasing as we move away from it.

5. How is divergence related to the flow of fluid in spherical coordinates?

Ans. In fluid dynamics, divergence plays a crucial role in understanding the flow of fluid in spherical coordinates. A positive divergence indicates that there is a source of fluid at the point, causing the fluid to flow outwards. On the other hand, a negative divergence indicates a sink, where the fluid is flowing inwards. By analyzing the divergence, we can gain insights into the behavior and patterns of fluid flow in spherical coordinates.

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Sep 21, 2025 Last updated

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