An electric dipole having a directed moment is situated at the origin, as shown in Fig. P6.6.2….

An electric dipole having a 8da9cc3d d03d 4b20 a740 fe7d93a04955directed moment 88cbaba4 b2a1 44bd b37b 4d1d424675c5 is situated at the origin, as shown in Fig. P6.6.2. Surrounding it is a spherical cavity of free space having radius a. Outside of the radius 14f1e55e 930f 47ef 80a4 dda4bb510661 is a linearly polarizable dielectric having permittivity 3f5e2e17 ea90 4218 a52e efc5b9cf834d.

Fig. P6.6.2

2846f8fd 594c 43f6 99c3 994b8ed739c7

(a) Determine 8c950506 b65c 4b97 b747 22ec004c9c07 and a5d50a4f 61a0 4925 9481 0c45d1c5f065 in regions (a) and (b) outside and inside the cavity.

(b) Show that in the limit where 3f5e2e17 ea90 4218 a52e efc5b9cf834d 4222bd9b aa61 4aa6 8b35 3fcd0e409809 the electric field intensity tangential to the interface of the dielectric goes to zero. That is, in this limit, the effect of the dielectric on the interior fields is the same as if the dielectric were a perfect conductor.

(c) Show that the same interior potential is obtained as in the limit 3f5e2e17 ea90 4218 a52e efc5b9cf834d 9ba68675 e2ab 44ff be6c 789781e9d4ad if this boundary condition is used at the outset.

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