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Review of Vector Calculus with special reference to Magnetic Field Theory
並列摘要
To build up a few properties of the attractive field, we must survey a portion of the standards of vector math. These standards will be our direction in the following segment. Consider a three dimensional vector field characterized by F = (P, Q, R) , where P , Q and R are all elements of x , y and z . A run of the mill vector field, for instance, would be F = (2x, xy, z 2 x) . The disparity of this vector field is characterized as: div F= ∂P/∂x+∂Q/∂y+∂R/∂z. Accordingly the disparity is the total of the incomplete differentials of the three capacities that constitute the field. The difference is a capacity, not a field, and is characterized exceptionally at every point by a scalar. Talking physically, the disparity of a vector field at a given point measures whether there is a net stream toward or away the point. It is frequently helpful to make the relationship contrasting a vector field with a moving waterway. A nonzero difference demonstrates that sooner or later water is presented or detracted from the framework (a spring or a sinkhole). Review from electric strengths and fields that the disparity of an electric field at a given point is nonzero just if there is some charge thickness by then. Point charges cause dissimilarity, as they are a ＂source＂ of field lines.