s-[2+D2-2rDcos,s[b+r2-2rbcoso r=R=0÷g-(g-( q2s2=q2s2q2R2+D2-2RD cos0=q2b2+R2-2Rbcos0 q2(R2+D2)=q2(b2+R2） g心Z0os-70as雨一g-8 BR2)-8R2-2-6g0小R2-0 o-0-)-0 6、R2 D D2→q'=-qR/D force on sphere qq' -q"R/D -q2RD 4πe(D-b)2 4π80 R2 4(D2-R27 2.Isolated Sphere [Put additional Image Charge +q'=+qR/D at center] (zero charge) Φ(r=R)=,g'=q 4xEoR4xED 6.641,Electromagnetic Fields,Forces,and Motion Lecture 5 Prof.Markus Zahn Page 4 of 116.641, Electromagnetic Fields, Forces, and Motion Lecture 5 Prof. Markus Zahn Page 4 of 11 0 1 q q' 4 s s' ⎛ ⎞ Φ= + ⎜ ⎟ πε ⎝ ⎠ = + − θ = +− θ ⎡ ⎤⎡ ⎤ ⎣ ⎦⎣ ⎦ 1 1 2 2 2 22 2 s r D 2rD cos , s' b r 2rb cos ( ) 2 2 q q' q q' rR 0 s s' s s' − ⎛⎞ ⎛ ⎞ Φ= =⇒ = ⇒ = ⎜⎟ ⎜ ⎟ ⎝⎠ ⎝ ⎠ 2 2 22 2 2 2 2 2 2 q s ' q' s q' R D 2RD cos q b R 2Rb cos = ⇒ + − θ= + − θ ⎡ ⎤ ⎡ ⎤ ⎣ ⎦ ⎣ ⎦ ( ) ( ) 2 2 2 22 2 q' R D q b R += + 2 +q' 2 RD cos θ 2 = +q 2 Rb cos θ 2 2 q' b q D ⇒ = ( ) 2 b R 22 22 2 2 RD bR bb DR 0 D D ⎛ ⎞ + =+⇒− ++ = ⎜ ⎟ ⎝ ⎠ ( ) 2 R bDb 0 D ⎛ ⎞ − ⎜ ⎟ − = ⎝ ⎠ 2 R b D = 2 22 2 2 b R q' q q q' qR D D D = = ⇒ =− force on sphere ( ) ( ) 2 2 x 22 2 2 2 2 0 0 0 qq' q R D q RD f 4 Db R 4 DR 4 D D − − == = π − ⎛ ⎞ π − π − ⎜ ⎟ ⎝ ⎠ ε ε ε 2. Isolated Sphere [Put additional Image Charge +q' qR D = + at center] (zero charge) ( ) 0 0 q' q r R 4R4D Φ= = = π π ε ε