# by Nannapaneni Narayana Rao Edward C. Jordan Professor of Electrical and Computer Engineering - PowerPoint PPT Presentation

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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

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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

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

• 1.4

• Scalar and Vector Fields

• 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.

• (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).

• Example: Linear velocity vector field of points on a

• rotating disk

• (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)

• D1.10 T(x, y, z, t)

• (a)

• Constant temperature surfaces are elliptic cylinders,

• (b)

• Constant temperature surfaces are spheres,

• (c)

• Constant temperature surfaces are ellipsoids,

• 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.

• Similarly

cylindrical

spherical

• P1.26(b)

(Position vector)

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