A point charge finds itself at a height above an infinite half-space of dielectric material. The…

A point charge finds itself at a height 020e5b8b 6f46 4ef9 91c7 b47b808ee7a9 above an infinite half-space of dielectric material. The charge has magnitude 2dca05eb c9b1 48ff b848 1552e8d65fac, the dielectric has a uniform permittivity 8945d4f8 fd23 4bbd af30 2903c558c43c, and there are no unpaired charges in the volume of the dielectric or on its surface. The Cartesian coordinates 044a0200 9c7c 4577 8258 78283a471c67 and 55bdcf8f 0a7c 4b09 bfbe d2194a426da9 are in the plane of the dielectric interface, while y is directed perpendicular to the interface and into the free space region. Thus, the charge is at 57d93103 872f 4b9d 85c1 270f50928a68. The field in the free space region can be taken as the superposition of a particular solution due to the point charge and a homogeneous solution due to a charge 06a85f48 bea3 4a8f 8634 6fc36b623a0d at d4c0e223 0609 4087 ace6 bed0a5de7036 below the interface. The field in the dielectric can be taken as that of a charge 7dc97af6 a71b 495f 843e 98a2376c183e at 57d93103 872f 4b9d 85c1 270f50928a68.

(a) Show that the potential is given by

d166deb3 19d7 4313 b940 43f26eb08212

(b) Show that the charge is attracted to the dielectric with the force

d3b19962 b4c1 4268 a157 8a11c8126e84

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