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

1.6 The Magnetic Field

The Magnetic Field acts to exert force on charge when it is in motion. B = Magnetic flux density vector Alternatively, since charge in motion constitutes current, magnetic field exerts forces on current elements.

Units of B: Sources: Currents; Time-varying electric field

Ampère’s Law of Force

Magnetic field due to a current element (Biot-Savart Law) B circular to the axis of the current element

Ex.

Current Distributions Filamentary Current I (A) (b) Surface Current Surface current density, JS (A/m)

(c) Volume Current Density, J (A/m2)

P1.44 a1 a a2 P(r, f, z)

For infinitely long wire,

Magnetic Field Due to an Infinite Plane Sheet of Uniform Surface Current Density This can be found by dividing the sheet into infinitely long strips parallel to the current density and using superposition, as in the case of finding the electric field due to an infinite plane sheet of uniform surface charge density. Instead of going through this procedure, let us use analogy. To do this, we first note the following:

Point Charge Current Element

(b) Line Charge Line Current rL0

(c) Sheet Charge Sheet Current Then, (c) Sheet Charge Sheet Current rS0