force on sphere q g' qq'D2-(D-b)-q'R[2bD-b2] fx= '7 4e0 1(D-b2 D2 4xoD2 (D-b)2 4p0-g】 -q'RD2 o R2[ -q2R3 4xEoD (D2-R2)2 D 48D2(D2-R2 [2D2-R2] qR D -qR/D ←b→ D 6.641,Electromagnetic Fields,Forces,and Motion Lecture 5 Prof.Markus Zahn Page 5 of 116.641, Electromagnetic Fields, Forces, and Motion Lecture 5 Prof. Markus Zahn Page 5 of 11 force on sphere ( ) ( ) ( ) 2 2 2 2 x 2 2 2 2 2 2 0 0 3 0 qq' D D b q R 2bD b q q' q' f 4 D b D 4 DDb R 4 DD D ⎡ ⎤ ⎡ ⎤ − − − − ⎡ ⎤ ⎢ ⎥ ⎣ ⎦ ⎣⎦ = − ⎢ ⎥ = = π ⎢ ⎥ − π− ⎛ ⎞ ⎣ ⎦ π − ⎜ ⎟ ⎝ ⎠ ε ε ε ( ) ( ) 22 2 2 2 3 2 2 x 2 2 32 2 32 2 0 0 q RD R R q R f 2D 2D R D D 4 DD R 4 DD R − − ⎡ ⎤ = − = − ⎡ ⎤ ⎢ ⎥ ⎣ ⎦ π − ε ε ⎢ ⎥ ⎣ ⎦ π −