Electrical Engineering (EE) Exam > Electrical Engineering (EE) Videos > Electromagnetic Fields Theory (EMFT) > Curl-Grad, Div & Curl
Curl-Grad, Div & Curl Video Lecture | Electromagnetic Fields Theory (EMFT) - Electrical Engineering (EE)
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10 videos|45 docs|56 tests
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FAQs on Curl-Grad, Div & Curl Video Lecture - Electromagnetic Fields Theory (EMFT) - Electrical Engineering (EE)
| 1. What is curl in vector calculus? |  |
Ans. Curl is a vector operator that represents the rotation of a vector field. It measures the circulation of a vector field around a point, indicating how much the vector field is swirling or rotating at that point.
| 2. How is curl calculated? | |
Ans. The curl of a vector field can be calculated using the curl operator. In Cartesian coordinates, the curl of a vector field F = (F_x, F_y, F_z) is given by the determinant of a matrix:
curl(F) = (dF_z/dy - dF_y/dz, dF_x/dz - dF_z/dx, dF_y/dx - dF_x/dy)
where dF_x/dy represents the partial derivative of F_x with respect to y, and so on.
| 3. What does the divergence of a vector field represent? | |
Ans. The divergence of a vector field measures the rate at which the vector field is spreading or diverging from a given point. It represents the total outgoing flux from an infinitesimally small closed surface surrounding the point.
| 4. How is divergence calculated? | |
Ans. The divergence of a vector field F = (F_x, F_y, F_z) can be calculated using the divergence operator. In Cartesian coordinates, the divergence of F is given by the sum of the partial derivatives of its components:
div(F) = dF_x/dx + dF_y/dy + dF_z/dz
where dF_x/dx represents the partial derivative of F_x with respect to x, and so on.
| 5. What is the relationship between curl and divergence? | |
Ans. The relationship between curl and divergence is given by the vector calculus identity known as the "curl of the curl" or "Laplacian of a vector field". It states that the curl of the curl of a vector field is equal to the gradient of the divergence minus the Laplacian of the vector field. In equation form:
curl(curl(F)) = grad(div(F)) - ∇^2(F)
This relationship shows the interplay between the rotation (curl) and spreading (divergence) of a vector field.
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Dec 22, 2024 Last updated |
Video Description: Curl-Grad, Div & Curl for Electrical Engineering (EE) 2024 is part of Electromagnetic Fields Theory (EMFT) preparation.
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