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 r q v Ampere-Maxwell Law Faradays Law Summarized in Maxwell equations = r r E q F E = r r r B q F v B = + r r r r q q F E v B Lorentz force Math -- review = & r r r C A B Vector cross product: r A r B = & r r r C A B Vector cross product: = & = - r r r r D B A C r A r B = r r r D A B ( 29 sin i = r C AB C Determine the direction. If Magnitude of the vector : r C = & r r r 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: r r = r 2 1 4 dq d r E r r r r d E dq P From Biot-Savart's Law , a point current generates magnetic field distance away from the source: r Id s r r r d B r Id s = r r 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. r Id s r d B Total Magnetic Field is the field created by the current in the length segment , a vector that takes the direction of the current. To find the total field, sum up the contributions from all the current elements The integral is over the entire current distribution o = 4 x 10-7 T . m / A , is the constant o is called the permeability of free space d B r i = r r 2 4 o Id r s r B r Id s r d s Example: from a Long, Straight Conductor with current I The thin, straight wire is carrying a constant current I Constructing the coordinate system and place the wire along the x-axis, and point P in the X-Y plane....
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chapter30 - Chapter 30 Sources of the Magnetic Field A...

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