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Edward C. Jordan Memorial Offering of the First Course under the Indo-US Inter-University Collaborative Initiative in Higher Education and Research: Electromagnetics for Electrical and Computer Engineering. by Nannapaneni Narayana Rao

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By nannapaneni narayana rao edward c jordan professor of electrical and computer engineering

Edward C. Jordan Memorial Offering of the First Course under the Indo-US Inter-University Collaborative Initiative in Higher Education and Research: Electromagnetics for Electrical and Computer Engineering

by

Nannapaneni Narayana Rao

Edward C. Jordan Professor of Electrical and Computer Engineering

University of Illinois at Urbana-Champaign

Urbana, Illinois, USA

Amrita Viswa Vidya Peetham, Coimbatore

July 10 – August 11, 2006


By nannapaneni narayana rao edward c jordan professor of electrical and computer engineering

  • 1.4

  • Scalar and Vector Fields


By nannapaneni narayana rao edward c jordan professor of electrical and computer engineering

  • FIELD is a description of how a physical quantity varies from one point to another in the region of the field (and with time).

  • (a)Scalar fields

  • Ex:Depth of a lake, d(x, y)

  • Temperature in a room, T(x, y, z)

  • Depicted graphically by constant magnitude contours or surfaces.


By nannapaneni narayana rao edward c jordan professor of electrical and computer engineering

  • (b)Vector Fields

  • Ex:Velocity of points on a rotating disk

  • v(x, y) = vx(x, y)ax + vy(x, y)ay

  • Force field in three dimensions

  • F(x, y, z)=Fx(x, y, z)ax + Fy(x, y, z)ay

  • + Fz(x, y, z)az

  • Depicted graphically by constant magnitude contours or surfaces, and direction lines (or stream lines).


By nannapaneni narayana rao edward c jordan professor of electrical and computer engineering

  • Example: Linear velocity vector field of points on a

  • rotating disk


By nannapaneni narayana rao edward c jordan professor of electrical and computer engineering

  • (c)Static Fields

  • Fields not varying with time.

  • (d)Dynamic Fields

  • Fields varying with time.

  • Ex:Temperature in a room, T(x, y, z; t)


By nannapaneni narayana rao edward c jordan professor of electrical and computer engineering

  • D1.10 T(x, y, z, t)

  • (a)

  • Constant temperature surfaces are elliptic cylinders,


By nannapaneni narayana rao edward c jordan professor of electrical and computer engineering

  • (b)

  • Constant temperature surfaces are spheres,

  • (c)

  • Constant temperature surfaces are ellipsoids,


By nannapaneni narayana rao edward c jordan professor of electrical and computer engineering

  • Procedure for finding the Equation for the Direction Lines of a Vector Field

The field F is

tangential to the

direction line at

all points on a

direction line.


By nannapaneni narayana rao edward c jordan professor of electrical and computer engineering

  • Similarly

cylindrical

spherical


By nannapaneni narayana rao edward c jordan professor of electrical and computer engineering

  • P1.26(b)

(Position vector)


By nannapaneni narayana rao edward c jordan professor of electrical and computer engineering

  • \ Direction lines are straight lines emanating radially from the origin. For the line passing through (1, 2, 3),


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