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1、2-1Engineering ElectromagneticsW.H. Hayt, Jr. and J. A. BuckChapter 2Coulombs Law and Electric Field Intensity2-2Coulombs Experimental Law+Q1Q2RFForce of repulsion, F, occurs when charges have the same sign. Charges attract when of opposite signwhere2-3Free Space Permittivitywith which the Coulomb f
2、orce becomes:2-4Coulomb Force with Charges Off-Origin2-5Electric Field IntensityConsider the force acting on a test charge, Qt , arising from charge Q1:where a1t is the unit vector directed from Q1 to Qt The electric field intensity is defined as the force per unit test charge, orN/CA more convenien
3、t unit for electric field is V/m, as will be shown.t2-6Electric Field of a Charge Off-Origin2-7Superposition of Fields From Two Point ChargesFor n charges:2-8ExampleFind E at P, usingFirst, find the vectors:Then: 2-9Example (continued)Find E at P, usingNow:so that:where2-10Volume Charge DensityGiven
4、 a charge Q within a volume , the volume charge density is defined as:.so that the charge contained within a volume is 2-11ExampleFind the charge contained within a 2-cm length of the electron beam shown below,in which the charge density is 32-12Example (continued)Q2-13Electric Field from Volume Cha
5、rge DistributionsNext, sum all contributions throughout a volume and take the limit as approaches zero, to obtain the integral:2-14Line Charge Electric FieldLine charge of constant density L Coul/m lies along the entire z axis.At point P, the electric field arising from charge dQ on the z axis is:wh
6、ereso thatThereforeand2-15Line Charge Field (continued)We have:By symmetry, only a radial component is present:2-16Line Charge Field Results2-17Example: Off-Axis Line ChargeWith the line displaced to (6,8), the field becomes:whereFinally:2-18Sheet Charge FieldUniform surface charge of density s cove
7、rs the entire y-z plane.We begin by writing down the line charge field on the x axis for a strip of differential width dy, where we consider the x component of that field:The total field on the x axis is:or2-19Types of Streamline Sketches of Fields:2-20Methodology of Streamline ConstructionThe ratio of the y and x field components gives the slopeof the field plot in the x-y plane2-21Example: Line Charge FieldBegin with the normalized line charge field in cylindrical coordinates:Convert to rectangular components:Thenwhose solution isFinally