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March 10, 2021 • 17:03 pm 30 points

Unit-4 electromagnetic theory-1 4.1 mathematics required for emt in order to proceed in electromagnetic theory we have to understand some basic concepts of math

Unit-4 Electromagnetic Theory-1 4.1 MATHEMATICS REQUIRED FOR EMT In order to proceed in Electromagnetic theory we have to understand some basic concepts of mathematical operations. So, we are proceeding by ntroduction of these concepts. Gradient If o(x. y. 2) be a scalar function then gradient of the scalar function s delined as (in Gartesian coordinates) grad- R ay Z grad = xy.2) grad V Geometrical Meaning of Gradient, Normal if a surface d(X, y, 2)= C passes through a pointP The value of the function at each point on the surface is the same as at P Then such a surtace is called a level surtface through P. For example, if Gx. y. 2) represents potential at the point P, then equipotential surtace o(%, y, Z) = CIs a level surface Two level surtaces Can not intersect. Let the level surtace pass through the point P at which the value of the function is . Consider another level surface passing througn C, wnere tne value Or the Tunction is + do. Let r and r+ör be the position vector of P and Q then PQ=ör a d6=c 8n Vo-dr |(idx+ jdy+ kdz) dxdydz-d (1) fa lies on the level surface of P, then dy = 0 Equation (1) becomes, Vo dr= 0, then Vo Is perpendicular to dr (tangent) Hence, Vo 1s normal to the surtace p(x, Y, 2)= C Weboite www.eduncle.com Email supporteduncle.com |Call Us: 7665435300 466

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