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1、Chapter 2 Electrostatic field & constant current 2.1 electrical field intensity & constant field,Couloms Law is the basic experimental law of electrostatic phenomenon,indicating that the two point electric charges setting on two places with the distance R has the interaction force：being in direct pr
2、oportion to the product of their quantity of electric charges, being in the inverse ratio of their squared distance.The direction of the force is along the connection line of the two point.Like charges repel each other,unlike charges attract.The expression is,2.1.1 Coulombs Law,2.1 interaction force
3、 of two point charges,This statement is Coulombs Law in its conceptual form.,The electrical field intensity of point chargeAssume:q is the point charge setting on point S(x,y, z), and introduce test charge qt at point P(x,y, z), shown in Fig 2-2 .According to Coulombs Law, if the force on qt is , th
4、e electric Field Intensity at the point is,2.1.2 Electrical field,Fig 2-2 field point & source point,The observation point P is called field point . Its position is represented by (x, y, z) or r. The point charge setting place S is called source point.Its position is represented by (x,y, z) or r. Th
5、e distance vector between source point and field point can be represented by R=r-r. In RCS，R=ax(x-x)+ay(y-y)+az(z-z)，and its value can be calculated by,Therefore, the equation canalso be represented by,When there are n point charges, the electric Field Intensity of field point equals to vector sum o
6、f the electric Field Intensity of each point charge ，i.e.,Assuming that charges converge at a certain point, seen from a macroscopic perspective, charges are distributed continuously on a line, a surface or in a volume. linear charge density（Charge Line Density）: when charges are distributed on a fi
7、neline （the ratio of lateral dimension to length is very small）, charges on the unit length is defined to be Charge Line Density:,Where，q is the charge of length microelementl.,2. the electric Field Intensity of distributed charges,density of surface charge（Charge Areal Density）: when charges are di
8、stributed on a surface , charges on the unit surface is defined to be Charge Line Density:,where， q is the charge of surface microelementS.,Density of volume charge（Charge Volume Density）:when charges are distributed in a volume, charges on the unit surface is defined to be Charge Line Density:,wher
9、e, q is the charge of volume microelementV,2.3 The field generated by volume charge,The electric Field Intensity of distributed charges :Asume that charges are distributed in volumeV with a densityV(r). take a volume microelement dV in V, shown in the above figure. the charges in the volume microele
10、ment is dq=V(r)dV, and is regarded as point electric charge. Then the electrical field intensity at field point P(r):,In volume V, the total electric field generated by all the charges at P(r),In a similar manner, when charge distribution is ,The electric field intensity can be calculated by,The equ
11、ations are called integration formulas of electric field intensity. When charge distribution is given, electric field intensity can be calculated.,Example: line charge with linear densityl on the straight line l with finite length, shown in Fig. 2.4. Calculate the electric field intensity in the fie
12、ld.,2.4 the straight line with finite length,2.5 the straight line with infinite length,In electrostatic field, electric potential at some point P is defined as the work done by electrostatic force on unit positive charge from Point P to reference point Q. If the work done by electrostatic force onT
13、est positive charge qt from Point P to reference point Q is W，the potential function P is,2.1.3 potential function,If the charge cant extend to infinite point, reference point Q is usually taken at infinite point. This method is convienent for the calculation of potential function. Here, the electri
14、c potentialan arbitrary point is,Electric potential expression of the point electric charge is,According to the expression electric potential at infinite point is zero.,The relationship between electric potential and electric field intensity is E= -,If the charges are distributed in volume V with a
15、volume densityV(r),the electric-field intensity generated by the charges is,Similarly, when the charge distribution is S(r) or l(r), the expression of potentiometric function is,Example. In vacuo, the charges of a conducting sphere with charge, whose radius is a , is Q. Please calculate the electric
16、 potential and electric field intensity。,isolated conducting sphere with charge,the field distribution of a conducting sphere with charge,Electric dipole is a pair of closely charges with the same electric quantity & different sign.Assuming the electric quantity of every charge is q, the distance of the two charges is d，shown in Fig 。Calculate the electric potential and electric field intensityof the electric dipole at Point P in spherical coordinates. According to the electric potential of point electric charge expression, the electric potential of eelectric dipole at P is,
