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Divergence & Curl of vector field Video Lecture | Mathematics for Competitive Exams
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FAQs on Divergence & Curl of vector field Video Lecture - Mathematics for Competitive Exams
| 1. What is the divergence of a vector field? |  |
Ans. The divergence of a vector field is a scalar quantity that measures the rate at which the vector field's flow is spreading or converging at a particular point. It is calculated using the dot product of the vector field with the del operator (∇).
| 2. How is the divergence of a vector field calculated? | |
Ans. The divergence of a vector field F = (F₁, F₂, F₃) is calculated using the formula ∇ · F = ∂F₁/∂x + ∂F₂/∂y + ∂F₃/∂z, where ∂/∂x, ∂/∂y, and ∂/∂z are the partial derivatives with respect to the respective variables.
| 3. What does a positive divergence value indicate? | |
Ans. A positive divergence value indicates that the vector field is spreading outwards from the point of interest. In other words, the flow is diverging away from the point.
| 4. What is the curl of a vector field? | |
Ans. The curl of a vector field measures the tendency of the vector field's flow to circulate or rotate around a point. It is a vector quantity and is calculated using the cross product of the vector field with the del operator (∇).
| 5. How is the curl of a vector field calculated? | |
Ans. The curl of a vector field F = (F₁, F₂, F₃) is calculated using the formula ∇ × F = (∂F₃/∂y - ∂F₂/∂z, ∂F₁/∂z - ∂F₃/∂x, ∂F₂/∂x - ∂F₁/∂y), where ∂/∂x, ∂/∂y, and ∂/∂z are the partial derivatives with respect to the respective variables.
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Dec 23, 2024 Last updated |
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