III.Demonstration 4.7.1-Charge Induced in Ground Plane by Overhead Conductor ⊙ Amp X Area A a-R Figure 4.7.2 Charge induced on ground plane by overhead conductor is measured Y10 by probe.Distribution shown is predicted 4 321 0--2-3-4 by(4.7.7. Courtesy of Hermann A.Haus and James R.Melcher.Used with permission. Φ=U R ·-入 a=12-R2 入 fe-srp.n0-xr I 2RE0 [a*x2+y2 4e0 (a+x2+y2 C'= 入 280 Φ(x=1-R,y=0) 元Ina-1+R Φ(x=1-R,y=0)=U -R2+i 2xEoa+1-R In R 6.641,Electromagnetic Fields,Forces,and Motion Lecture 5 Prof.Markus Zahn Page 6 of 116.641, Electromagnetic Fields, Forces, and Motion Lecture 5 Prof. Markus Zahn Page 6 of 11 III. Demonstration 4.7.1 – Charge Induced in Ground Plane by Overhead Conductor Courtesy of Hermann A. Haus and James R. Melcher. Used with permission. ( ) ( ) ( ) ( ) 1 2 2 2 2 2 1 2 2 0 0 2 2 2 ax y ax y ln ln 2 4 ax y ax y ⎡ ⎤ − + ⎡ ⎤ −λ −λ ⎢ ⎥ − + ⎣ ⎦ Φ= = ⎢ ⎥ π π ⎢ ⎥ ⎡ ⎤ + + + + ⎣ ⎦ ⎢ ⎥ ⎣ ⎦ ε ε ( ) ( ) λ λ π = = = Φ =− = = Φ =− = −λ − + ⎡ ⎤ − + ⎢ ⎥ π +− ⎢ ⎥ ⎣ ⎦ ε ε 0 2 2 0 2 C ' , x l R, y 0 U x l R, y 0 alR ln lR l 2 alR ln R