chapter30

# chapter30 - Chapter 30 Sources of the Magnetic Field A...

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Unformatted text preview: Chapter 30 Sources of the Magnetic Field A whole picture helps Charge q as source Current I as source Electric field E Magnetic field B Gausss Law Amperes Law Force on q in the field Force on or I in the filed a q v Ampere-Maxwell Law Faradays Law Summarized in Maxwell equations = a a E q F E = a a a B q F v B = + a a a a q q F E v B Lorentz force Math -- review = a a a C A B Vector cross product: a A a B = a a a C A B Vector cross product: = = - a a a a D B A C a A a B = a a a D A B ( ) sin = a C AB C Determine the direction. If Magnitude of the vector : a C = a a a B F v B The right-hand rule: 1. Four fingers follow the first vector. 2. Bend towards the second vector. 3. Thumb points to the resultant vector. Sources of Electric field, magnetic field From Coulomb's Law, a point charge dq generates electric field distance away from the source: a r = a 2 1 4 dq d r E r a r a d E dq P From Biot-Savart's Law , a point current generates magnetic field distance away from the source: a Id s a r a d B a Id s = a a 2 4 Id d r s B r Difference: 1. A current segment , not a point charge dq , hence a vector. 2. Cross product of two vectors, is determined by the right-hand rule. a Id s a d B Total Magnetic Field c is the field created by the current in the length segment , a vector that takes the direction of the current. c To find the total field, sum up the contributions from all the current elements c The integral is over the entire current distribution c o = 4 x 10-7 T . m / A , is the constant o is called the permeability of free space d B a = a a 2 4 o Id r s r B a Id s a d s Example: from a Long, Straight Conductor with current I c The thin, straight wire is carrying a constant current I c Constructing the coordinate system and place the wire along the x-axis, and point P in the X-Y plane....
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## This note was uploaded on 05/06/2008 for the course PHYS 1304 taught by Professor Ye during the Spring '08 term at SMU.

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chapter30 - Chapter 30 Sources of the Magnetic Field A...

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