《Electromagnetism, principles and application》教学课件（PPT讲稿）Chapter 1 Vectors

Electromagnetism 2004 Fall Reference K Electromagnetism principles and application > by p lorrain d Corson

Electromagnetism 2004 Fall Reference: 《 Electromagnetism, principles and application》 by P.Lorrain & D.Corson

Chapter 1 Vectors Object: to describe the fieds generated by electric charges and currents Mathematical tools A field is a function describing a quantity at all points in space

Chapter 1 Vectors ◼ Object: to describe the fieds generated by electric charges and currents ◼ Mathematical Tools: A field is a function describing a quantity at all points in space

Several kinds scalar fields vector fields tensor fields scalar fields: a single number is given for each point in space well known to us Example: temperature, pressure, electric potential, etc

Several kinds : scalar fields, vector fields, tensor fields ◼ scalar fields: a single number is given for each point in space ---- well known to us. Example: temperature, pressure, electric potential, etc

Tensor are necessary to unify electric and magnetic fields to describe the gravitational fields in Einstein' s Theory of General relativity; to deal with strain and stress in solids eto

Tensor are necessary : to unify electric and magnetic fields; to describe the gravitational fields in Einstein’s Theory of General Relativity; to deal with strain and stress in solids, etc

We focus on vector fields Vector fields: both a number and a direction at all point in space Examples: electric fields, magnetic fields, current fields of fluid etc

We focus on vector fields ◼ Vector fields: both a number and a direction at all point in space. Examples: electric fields, magnetic fields, current fields of fluid, etc

a vector: A= Axi+ Auj+ A2k components: AC,Ay,A2 unit vectors: i,j,k addition: A+B=(Ax+ Bx)i+(Ay+Byj(A2+ Byk and subtraction A-B=(Ax-Bxrji+(Ay- Byj+(Az-Byk scalar product(dot product) A B=B A=ArBr+AyBy+ ABx A·B= AB cos6 where 0 is the angle bwtn a and B

A k Figure 1-2 A vector A and the three vectors A, i, A, j, A, k, which, when placed end-to-end, are equivalent to A

vector product(cross product) A×B=-B×A=C, Which is a vector whose direction: l to the plane containg A and b(right and rule magnitude: C=AB sin 0 explicitly A×B=(AyB2-A2Byi (1) +(A2 Bx- B2)j +(ArBy-AgBrkk

Time derivative of a vector da dAr, dAy. dAz 1+ +-k dt dt Which is a vector More important is the gradient of a scalar function sa tine af. af. af j+。k dx du az Which is a vector 0-“ partia| For instance. the electrostatic field e can be constructed out of the electric potential E=-VV

an application of gradient the change of f over a small displacement dl= dai+dyj+dik n space: af, af df =o dx + d Vf.dr=Vflldl cos 9