Curl-Grad, Div & Curl Video Lecture | Electromagnetic Fields Theory (EMFT) - Electrical Engineering (EE)

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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.
11 videos|45 docs|73 tests

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