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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

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by Nannapaneni Narayana Rao Edward C. Jordan Professor of Electrical and Computer Engineering

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  1. 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

  2. 1.4 • Scalar and Vector Fields

  3. 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.

  4. (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).

  5. Example: Linear velocity vector field of points on a • rotating disk

  6. (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)

  7. D1.10 T(x, y, z, t) • (a) • Constant temperature surfaces are elliptic cylinders,

  8. (b) • Constant temperature surfaces are spheres, • (c) • Constant temperature surfaces are ellipsoids,

  9. 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.

  10. Similarly cylindrical spherical

  11. P1.26 (b) (Position vector)

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

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