电磁场与电磁波——矢量分析与场论.ppt

Chapter 1 Vector analysis&field theory1.1 Vectors algebra 1.Scalar,Vector&FieldScalar:,voltage,temperature,time,quality,electric charge Only Value&Unit Scalar field:the set of scalars with the same category and infinite numberVector:,electrical field intensity，magnetic field intensity，force，moment of force Value,Unit&direction Vector field:the set of vectors with the same category and infinite number1 Chapter 1 Vector analysis&field theory1.1 Vectors algebra1.Scalar,Vector&FieldField:Scalar field,Vector field,tensor field 1.continuous distribution of physical quantity in certain space2.actually exist 3.The space of a certain property,have energy,transfer interaction 22.Vectors algebra1).Representation of vector(in rectangular coordinate system)Null Vector(Zero Vector),Unit VectorThe point P(X,Y,Z)is represented by .is called Position Vector.Projection of P to coordinate axes 3Vector :the magnitude of A：A=(A2x+A2y+A2z)1/2 42).Vectors algebra (Vector )(1).Plus and minus(2).Product 52).Vectors algebra (Vector )(2).Product 6Important identical equations:Proof of the identical equations:Do-it-yourself Assignment:1.There are three vector,as follows:Please calculate:(1).Unit vector (2).The angle between(3).(4).7 Chapter 1 Vector analysis&field theory1.2-1.3 The cylindrical coordinate system&Spherical coordinate system Coordinate system xyrP(x,y,z)场点Rectangular coordinate system RCSz8Cylindrical coordinate system CCS9Spherical coordinate system SCS10Main content to learn1.Variables to present a point P in coordinate spacea).The relationship between RCS&CCSb).The relationship between RCS&SCSc).Orthogonal coordinate surfaces11Main content to learn1.Variables to present a point P in coordinate spacec).Orthogonal coordinate surfaces12Main content to learn2.Unit coordinate vectors:Relations of unit coordinate vectors&right-hand screw rule13Main content to learn2.Unit coordinate vectors:Relations of unit coordinate vectors&right-hand screw rule14Main content to learn2.Unit coordinate vectors:Relations of unit coordinate vectors&right-hand screw rule15Main content to learn3.Position vector4.The transformation between different coordinate systems（Vector)RCS to SCS:SCS to RCS:SCS to RCS:165.Length increment Lame constants:176.Surface area element181.31.3 Vector fieldVector fieldTo research the space distribution and variety laws:vector line of vector flux of vector field and divergence circulation of vector field and Curl19 1.3.1 line of vector The point P(x,y,z)is presented by A=A(P).In rectangular coordinate system：A=A(x,y,z)Assuming Ax,Ay,Az:1).are three vector-valued function coordinate components of A;2).have continuous first partial derivatives.A is also presented by:A=axAx(x,y,z)+ayAy(x,y,z)+azAz(x,y,z)Vector lines are certain curves:at every point on the lines,vectors of the field lie along its tangential line.E.g.:lines of force of electrostatic field,lines of force of magnetic field,streamlines of velocity field20 Assuming:P is any point on point on vector lines of the vector field its radius vector is ,Then:In RCS,is represented by Vector lines of the vector field meets the differential equationdo it yourself21 Ex 1:Assuming electric charge q is on the ordinate origin,the electrical field intensity at any point produced by this charge isWhere,&are constant and is the position vector of P.Please calculate the equation for vector lines of .22Answer：231.3.2 Flux and divergence of vector field1.Flux of vector field :vector field :surface area element :unit vector perpendicular to （normal vector）The vector of surface area element is The flux for passing through 241.3.2 Flux and divergence of vector field1.Flux and of vector field :vector field :surface area element :unit vector perpendicular to （normal vector）The flux for of passing through the whole surface is If S is a closed surface,the flux is251.3.2 Flux and divergence of vector field Physical significance of equation tapsewer flow out flow inSinkSourcePositive flowNegative flow=Net flow=Positive flow+Negative flow261.3.2 Flux and divergence of vector field2.Divergence of vector field :vector field :closed surface :point in :volume confined in When ,the limit adopted is If the limit of the expression is exit,the limit is called:Divergence of at 271.3.2 Flux and divergence of vector field2.Divergence of vector field :vector field :closed surface :point in :volume confined in Physical significance of equation In RCS,281.3.2 Flux and divergence of vector fieldHamilton operator Then 291.3.2 Flux and divergence of vector fieldsource point,sink point,non-source If ,the field is continuous or solenoidal.Divergence Theorem(Gauss Divergence Theorem)The volume integral of divergence equals to the surface integral of the vectors normal component along the closed surface bonding the volume.Assignment:1.16,P19 301.3.3 Circulation and Curl of vector field1.Circulation of vector field :vector field :close directing curve in The line integral of along ,is called CirculationPhysical significance of equation swirl source312.Curl(Rotation)of vector field :vector field :close directing curve in :surface area element closed by :point in When ,the limit adopted is If the limit of the expression is exit,the limit is called:Curl or rotation of at along 1.3.3 Circulation and Curl of vector field322.Curl(Rotation)of vector field :vector field :close directing curve in :surface area element closed by :point in Physical significance of equation In RCS,1.3.3 Circulation and Curl of vector field331.3.2 Flux and divergence of vector fieldHamilton operator Then 341.3.2 Flux and divergence of vector fieldRotational,Irrotational or Conservative Stokes Theorem The surface integral of vector s curl along of equals to the line integral of along the boundary of the surface.Assignment:1.17,P19 351.4 Fradient of scalar field1.4.1.Isosurface A surface composed of all the point with the same scalar value in the field is called isosurface.Scalar function ,Equation of isosurface：二.标量场的梯度2、梯度的物理意义361.4 Fradient of scalar field1.4.2.Directional Derivative&its calculationWhere,Where,cos,cos&cos are the direction cosines of .371.4 Gradient of scalar field1.4.3.Gradient of scalar fieldHamilton operator Laplace operator CCS,SCS:38（1）（2）Gradient is the normal vector of isosurface.（3）u 0 F=0 F=u u is the potential function of the scalar function.Properties of gradientAssignment:1.23,P2039Integral of gradient40Field Source:Divergence Source,Rotational SourceNonrotational field and nondivergent field are two basic vector fields.Every vector field is generated by both or one of the two kind of sources and can be presented by the summation of Nonrotational field and nondivergent.1.5 Fradient of scalar fieldDivergence Source:Scalar SourceRotational Source:Vector Source41