Question

Consider an electric dipole oriented in the -x direction, p=-qoi, and located at the point (0, 0, zo). A grounded conducting slab occupies the region everywhere below the x-y plane. a. What is the boundary condition at the surface of the conductor that must be satisfied? b. Describe the image charge(s) you would introduce in order to find the electric field in the region above the conductor. Now, using the method of images and assuming a point-like electric dipole, determine the electric field on the z axis above the conductor. Hint: It might be helpful to use the coordinate-free form for the electric field of a 1 E(r) = z[3(p. f) f – p] 47eoro "pure” dipole at the origin given by, Finally, determine the asymptotic electric field to leading order on the z axis for z >> Zo and, in one or two sentences, discuss the characteristics of the field. Hint: It might be helpful to rewrite your expression and then apply a general Taylor expansion for (1+x)".

Answer 1

Given that, . An electric dipole. oriented in -2 direchon •p=-qoi • Located at point (0,0,7) A grounded conduching slab occuples the region everywhere below the xy plane. a.) at the surface of conductor The is 1 Boundary condition 1(2,4,0) = 0 for all (x, y) by By symmetry we should put a oppositely onented dipole at %=-70 which will make the potential=0 at 7:0 . Hence image dipole would be >= qoi" % To

C) Electric field at a distance from the conduching slab Re) ' ਵ + + ਕ : * 2- ਲ - - HT€6. EZ + d) or >> 2 , 4 0 7) En) tre , kthਲ ' ਜ ਸ ਜੀ ਦੀ : ( ) - ਤਵੀ- HTTE (5) , ' ਜੀ Hence at large distance (2) will fall off line ) which is the feature of guadsopole teom. Hence at large distance these two dipoles will act like a quadropole.