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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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