1、11.1 A pair of equal but opposite charges +q and -q with separation l constitute an electric dipole .Find the electric field at a point on the bisecting line of an electric dipole and from it (rl).,11.2 A stright line of length L is uniformly charged with a linear density .Find the field at a point
2、on the bisecting plane of the line,Consider a charge element on a length element,11.3 A thin circlular ring of radius R is charged uniformly with a total charge q.Find the field at any point on the axis of the ring.,The direcion of field is along the axis .At the center of the ring ,E=0,At far point
3、s,a field of a point charge q,11.4 A thin circular disk of radius R is uniformly charged with a constant surface charge density .Find the field at any point on the axis of the disk.,When,Consider a charge ring of radius r and width dr on the disk .since the total charge on this ring is ,we get the f
4、ield produced by this ring at P from the result of the last example,11.5 A spherical surface of radius R is uniformly charged with a total charge q.Find the electric field distribution,The frux through this closed surface is,The total charge inside is,Gass law,So when,When,11.6 A sphere of radius R
5、is charged uniformly inside with a constant volume charge density(charge per unit volume) .Find the field distribution.,The total charge,Inside the sphere,Gass law,11.7 An initinitely long straight line is charged with constant linear charge density (charge per unit length).Find the field distributi
6、on around it.,So Gass law gives whence,Considering the field at a point P with a distancer from th eline .as the charge is distributed symmetrically to the OP, the resultant field at P must be directed perpendicular to the charged line. The magnitude E of the field must be the same at all points on
7、a cylinderical surface of radius OP .Now take a closed cylindrical surface of length l and radius r (=OP) around a segment of the charged line as our Gassian surface , as shown in Fig . The flux through the two bottoms of this can-like surface is zero. The flux through the lateral surface is simply
8、the area , times ,which is also the total flux through the closed Gassian surface .the charge enclosed in the surface is just,11.8 An infinitely large plane sheet is charged uniformly with constant surface charge density (charge per unit area) .Find the field disribution in both sides.,Due to plane
9、symmetry , the electri field on either side of the sheet ,whatever its magnitude may be ,must surely point perpendicular to the sheet .the field must have equal magnitude and opposite direction at at two points P and P equidistant from the sheet on opposite sides. Furthermore , because the sheet is
10、infinitely large, the field at all points on the two planes through P and P and parallel to the charged sheet must have also equal magnitude E. With these facts recognized ,we may take a cylinder ,as shown in fig.with P and P on the two bottoms respectively,Of cross-sectional area as our Gaussian su
11、rface. The flux is found only at the bottoms and of the same sign. The total flux through the closed surface is thus ,the charge enclosed is .Gass law gives hence,11.9 Two parallel, infinitely large ,uniformly charged plane sheets have equal but opposite surface charge densities and respectively .Fi
12、nd the field distribution of this systerm.,In regionIn regionIn region,SUMMARY,1.The fundamental properties of electric charges: two varieties of charge, quantization , conservation ,relaticistic invariance.,2.Coulombs law:Invacuum the force between two point charges at rest expressed asWhere The pe
13、rmittivity(or the dielectric constant)of vacuum,3.Electric field intensity:definition at rest 4.Principle of surperposition of electric field intensity:Electric field of a point charge at rest:Electrostatic field of a systerm of point charges:,5.Electric flux:6.Gausss law:,7.Typical electrostatic fields:,(inside),(outside),Uniformly charged solid sphere:,Uniformly charged spherical surface:,(inside),(outside),Uniformly charged infinite long line:,perpendicular to the line,Uniformly charged inifinite large plane sheet, in both sides :,perpendicular toperthe plane sheet,