V=Ol cose ou Is the module of dipole momentum 4兀cr The resultant field in Cartesian coordinate is therefore E- l 3cos6-1 x4兀E0 E=Ql cos sin 0 y4兀0 E.=0 (Pls. try using the formula for Field to prove above results)
2 4 0 cos r Ql V = Ql Is the module of dipole momentum The resultant field in Cartesian coordinate is therefore ) 3cos 1 ( 4 3 2 0 r Ql Ex − = 3 0 cos sin 4 r Ql Ey = E z = 0 (Pls. try using the formula for Field to prove above results)
1.4.2 Spherical shell with uniform surface charge o 4R2 Discussion: 1) The choice of coordinate P(X, y, Z) y P(0,0,) X ds=? d=2mRsn●Rd6 2)Calculate smartly 2R sin 0de 4兀C0s 4T6R2+r2-2Rrcos 0
1.4.2 Spherical shell with uniform surface charge 2 4 R Q = Discussion: 1) The choice of coordinate x y z P(x,y,z) ds=? x z y P(0,0,r) ds = 2Rsin •Rd 2) Calculate smartly + − = − = − 0 2 2 2 0 0 2 cos 2 sin 4 4 1 R r Rr R d r ds V s
V= g r>r(Equivalent to a point charge 46 r<r(Constant 4丌EnR Discussion: How about the electric field? 1.4 Tools for the calculation of electrostatic field 1.4. 1 Imaginary line of Electric field General rules a. From positive to negative b. Never cross C. E is proportional to the density of the lines
r Q V 0 4 = R Q V 0 4 = r R r R (Equivalent to a point charge) (Constant!! ) (Constant!!) Discussion: How about the electric field? 1.4 Tools for the calculation of electrostatic field 1.4.1 Imaginary line of Electric field: General rules: a. From positive to negative; b. Never cross; c. E is proportional to the density of the lines
Figure 2319(a)The electric field lines for two equal and opposite point charges (an electric dipole). Note that the number of lines leaving the positive charge equals the number terminating at the negative charge. (b)The photograph was taken using small pieces of thread suspended in oil, which align with the electric field. (Photo courtesy of Harold M. Waage, Princeton University) Figure 23.20(a)The electrie field lines for two positive point charges. (b) The photograph was taken using small pieces of thread suspended in oil, which align with the electric ield.(Photo courtesy of Harold M. Waage, Princeton University)
1.4.2 Review of the concept of solid angle(steradian efinition: dQ 小· comparing the plane angle, where dl .sin e Steradian Radiant Discussion: Solid angle at any point inside a closed surface: 4 Solid angle at any point outside a closed surface: 0 1.4.3 Gauss' theorem Consider a flux of e produced by a point charge Passing through element area ds
1.4.2 Review of the concept of solid angle (Steradiant) 2 0 r r ds d • Definition: = comparing the plane angle, where r dl d • sin = Steradiant Radiant Discussion: Solid angle at any point inside a closed surface: 4π. Solid angle at any point outside a closed surface: 0. 1.4.3 Gauss’ theorem Consider a flux of E Passing through element area ds Produced by a point charge