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

1.5 The Electric Field

1.5- The Electric Field is a force field acting on charges by virtue of the property of charge. Coulomb’s Law

D1.13(b) From the construction, it is evident that the resultant force is directed away from the center of the square. The magnitude of this resultant force is given by Q2/4pe0(2a2) Q2/4pe0(4a2) Q2/4pe0(2a2)

Electric Field Intensity, E is defined as the force per unit charge experienced by a small test charge when placed in the region of the field. Thus Units: Sources: Charges; Time-varying magnetic field

Electric Field of a Point Charge (Coulomb’s Law)

Constant magnitude surfaces are spheres centered at Q. Direction lines are radial lines emanating from Q. E due to charge distributions (a) Collection of point charges

Ex. a Electron (charge e and mass m) is displaced from the origin by D (<< d) in the +x-direction and released from rest at t = 0. We wish to obtain differential equation for the motion of the electron and its solution.

For any displacement x, is directed toward the origin, and

The differential equation for the motion of the electron is Solution is given by

Using initial conditions and at t = 0, we obtain which represents simple harmonic motion about the origin with period

(b) Line Charges Line charge density, rL (C/m) (c) Surface Charges Surface charge density, rS (C/m2) (d) Volume Charges Volume charge density, r (C/m3)

Ex. Finitely-Long Line Charge

Infinite Plane Sheet of Charge of Uniform Surface Charge Density rS0 a

rS0

D1.16 Given rS1 rS2 rS3

Solving, we obtain (a) (b) (c) (d)