u=r2+d2 du 2rdr rdr 37 「d=u为=-1 3/ [r2+ 2+ 92=o)=4 =-q -q2 f。-4co2d -q2 -16mEod2 II.Point Charge and Sphere 1.Grounded Sphere Conducting sphere at zero potential inducing chorgc b outside sphere (a) Inducing charge inside sphere g-8 g D D ) Figure 2-27 (a)The field due to a point charge q.a distance D outside a conducting sphere of radius R.can be found by placing a single image charge -gR/D at a distance b=RD from the center of the sphere.(b)The same relations hold true if the charge q is inside the sphere but now the image charge is outside the sphere,since D<R. Courtesy of Krieger Publishing.Used with permission. 6.641,Electromagnetic Fields,Forces,and Motion Lecture 5 Prof.Markus Zahn Page 3 of 116.641, Electromagnetic Fields, Forces, and Motion Lecture 5 Prof. Markus Zahn Page 3 of 11 2 2 u r d du 2rdr =+⇒ = 1 2 3 3 2 2 2 22 2 rdr du 1 u 2u r d r d − = =− =− ⎡ ⎤ + + ⎣ ⎦ ∫ ∫ T ( ) 2 2 0 qd qz0 q r d ∞ + = = =− + ( ) _ _ 2 2 q z 2 2 0 0 q q f i 4 2d 16 d − − = = πε πε II. Point Charge and Sphere 1. Grounded Sphere Courtesy of Krieger Publishing. Used with permission