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Electrodynamics (I): Homework 7 Due: Noverber 27, 2014 Exercises in Griffiths 4.24 (hand-in 10%), 4.26, 4.34, 4.37(hand-in 10%), 4.38, 4.39, 4.41 Ex.1 hand-in (a) 5% Suppose that the space for z > 0 is filled by a semi-infinite homogeneous dielectric with the dielectric constant being r . The space z ≤ 0 is filled by a grounded semi-infinite conductor. An electric dipole of moment p~ = p(sin φ, 0, cos φ) is placed at the position (0, 0, d) in the dielectric. Find the potential energy of the interaction between the electric dipole and the induced charge. In addition, find the torque that acts on the electric dipole and the force that acts on the electric dipole when the orientation of dipole is fixed. (b) 10% Suppose that except for a grounded conducting sphere of radius R whose center is at the origin, the space is filled with a homogeneous dielectric with the dielectric constant being r . An electric dipole of moment p~ = p(sin φ, 0, cos φ) is placed at the position (0, 0, d) outside the sphere along the z-axis. Determine the image charge distribution (in terms multipole moments) that can present the induced surface charge on the conducting sphere. Find the torque that acts on the electric dipole. Ex.2 hand-in 10% Two semi-infinite homogeneous dielectrics with dielectric constants κ1 and κ2 are in contact along an infinite plane. Two charges q1 and q2 are place at equal distances a from this plane along a straight line perpendicular to the plane. Find the forces that act one each of the charges. Are these two forces are equal? Explain why? 1