7. Suppose that you have an electric dipole with dipole moment p. In the lecture, we have found an electric field distribution in the far-field due to an electric dipole placed at origin with p pê, where î denotes a unit vector along the z-direction. Throughout this problem, assume that the dipole center is located at origin. (1) Find the far-field electric field distribution of an electric dipole p = pâ at r= (r, 0, 4). (2) Repeat (1) if p = pŷ. (3) If you do not know the exact direction of this dipole except that the likelihood among p = på, pŷ, and pê should be identical, what would be the electric field measured at r = (r, 0, 4)?

7. Suppose that you have an electric dipole with dipole moment p. In the lecture, we have found an electric field distribution in the far-field due to an electric dipole placed at origin with p pê, where î denotes a unit vector along the z-direction. Throughout this problem, assume that the dipole center is located at origin. (1) Find the far-field electric field distribution of an electric dipole p = pâ at r= (r, 0, 4). (2) Repeat (1) if p = pŷ. (3) If you do not know the exact direction of this dipole except that the likelihood among p = på, pŷ, and pê should be identical, what would be the electric field measured at r = (r, 0, 4)?