中国科学技术大学：《电磁学》课程教学资源（PPT课件讲稿）Chapter 1 Vectors

Electromagnetism 2004 Fall Reference K Electromagnetism principles and application by plorrain 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 a 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 a 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 i to deal with strain and stress in solids 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, etc

We focus on vector fields a 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= Ari+ Auj+A2 k components: Ar, Ay, Az unit vectors: i, j, k addition: A+B=(Ax+Bri+(Au+Bu)j+(A2+Bu)k and subtraction a-B=(Ar- Br)i+(Ay- By)j+(A2-By)k scalar product(dot product) A·B=B·A=ABx+ABn+A2B2 AB=AB COS 8, where g is the angle bwtn a and b

A i 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 g explicitly A×B=(AxB2-A2B +(A2)j +(A By- ayBrk

Time derivative of a vector: da dar. da. da i+=i+-k hich is a vector More important is the gradient of a scalar function ay, f sa D efine af. af af f=82 i+aj+。k, which is a vector partial For instance, the electrostatic field e can be constructed out of the electric potential v E=-VV

an application of gradient the change of f over a small displacement dl=dxi+dyj+dsk n space df af, af af dy+ dx Vf·dr=|Vfdl COS