8. Homework, Due on 13.08.2022: Method of Images A Point charge in front of a grounded...

 

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8. Homework, Due on 13.08.2022: Method of Images A Point charge in front of a grounded conducting plane Consider a point charge q at = = d near a grounded conducting plane extending from -x<=< 0, 2 (a) show that the potential at any point for = 20 is (r.y. =)= 4760 = [√²+²+(2-4)² = √²²+F²+(2+4)²] (= (b) find the electric field for 20 (c) show that the electric field is normal to the surface, (d) show that the total electric field at an arbitrary point of the conducting plane at := 0 is, (e) show that the induced charge density is, E(z.y.:=0)=- gd k 27 (2²+ y² +d²)3/2 d 2= (22+²+d2)3/2 (f) show that the total induced charge is equal to the image charge q = -q. Qind = (x,y) dzdy = -9 (g) show that the force of q' on q is, o(z. y)=E(x, y, z = 0)-k=-2 F=qE (0,0,d) 4mco (2d)² where E (0,0, d) is the electric field of the mirror charge o evaluated at the position of the charge q. (h) show that the electric field of q at any point on the conducting plane is, F E,(r.y.z=0)= zi+y) - dk Año (2²+ y² +d²)3/2 (i) consider an element of the induced charge dq" = o(z,y)drdy on the conducting plane such that, 9 d dq" = o(x,y)drdy=- 2=(2²+ y² +4²2)3/2 drdy show that the net force on all induced charges on the conducting plane is, [d²=ffd"E₂(x, y, == 0) q² dzi+yj-dk 4nto 2 (²+²+d²j³° dzdy k Απες (24)2 IL *P332, Department of Physics, Yarmouk University, Irbid, Jordan, Email: helga@yu.edu.jo, Office Hours (Room 349), 11:30-13:30 (Sunday) and 09:45-10.45 (Monday) 8. Homework, Due on 13.08.2022: Method of Images A Point charge in front of a grounded conducting plane Consider a point charge q at = = d near a grounded conducting plane extending from -x<=< 0, 2 (a) show that the potential at any point for = 20 is (r.y. =)= 4760 = [√²+²+(2-4)² = √²²+F²+(2+4)²] (= (b) find the electric field for 20 (c) show that the electric field is normal to the surface, (d) show that the total electric field at an arbitrary point of the conducting plane at := 0 is, (e) show that the induced charge density is, E(z.y.:=0)=- gd k 27 (2²+ y² +d²)3/2 d 2= (22+²+d2)3/2 (f) show that the total induced charge is equal to the image charge q = -q. Qind = (x,y) dzdy = -9 (g) show that the force of q' on q is, o(z. y)=E(x, y, z = 0)-k=-2 F=qE (0,0,d) 4mco (2d)² where E (0,0, d) is the electric field of the mirror charge o evaluated at the position of the charge q. (h) show that the electric field of q at any point on the conducting plane is, F E,(r.y.z=0)= zi+y) - dk Año (2²+ y² +d²)3/2 (i) consider an element of the induced charge dq" = o(z,y)drdy on the conducting plane such that, 9 d dq" = o(x,y)drdy=- 2=(2²+ y² +4²2)3/2 drdy show that the net force on all induced charges on the conducting plane is, [d²=ffd"E₂(x, y, == 0) q² dzi+yj-dk 4nto 2 (²+²+d²j³° dzdy k Απες (24)2 IL *P332, Department of Physics, Yarmouk University, Irbid, Jordan, Email: helga@yu.edu.jo, Office Hours (Room 349), 11:30-13:30 (Sunday) and 09:45-10.45 (Monday)

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Y x by Method of Images let conside there is an Image chare 2 below the plane at a distance 2 ... View the full answer