Chapter One: Vector Analysis The use of vectors and vector analysis ...

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Electromagnetic Theorem (Dr. Omed Ghareb Abdullah) University of Sulaimani –College of Science – Physics Department Problem: Prove that the curl of gradient is always zero. By equality of cross‐derivative: 0 20
Electromagnetic Theorem (Dr. Omed Ghareb Abdullah) University of Sulaimani –College of Science – Physics Department Integral Calculus: 1‐ Line integrals (Path): A line integral is an expression of the form, ∙ where is a vector function, is the infinitesimal displacement vector. And the integral is to be carried out along a prescribed path from point to point . If the path in question forms a closed loop (that is if ), I shall put a circle on the integral sign: ∙ Example of line integrals is the work done by a force : ∙ Ordinarily, the value of a line integral depends critically on the particular path taken from to . But if the line integral is independent of the path; a force that has this property is called Conservative. Example: Calculate the line integral of the function 2 1 from the point 1 ,1 , 0 to the point 2 , 2 , 0 along the paths 1 & 2 in Fig. What is ∮ ∙ for the loop that goes from to along 1 and returns to along 2?
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Chapter One: Vector Analysis The use of vectors and vector analysis ...

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