Field and Wave Electromagnetics 2nd Edition by David Cheng

تمرين 6

Two dielectric media with dielectric constants 1 and 2 are separated by a plane boundary at x = 0, as shown in Fig. A point charge Q exists in medium 1 at distance d from the boundary.
Figure: Image charges in dielectric media

a) Verify that the field in medium 1 can be obtained from Q and an image charge - Q 1 , both acting in medium 1.
b) Verity that the field in medium 2 can be obtained from Q and an image charge + Q 2 coinciding with Q, both acting in medium 2.
c) Determine Q 1 and Q 2 (Hint: Consider neighboring points P 1 and P 2 in media 1 and 2, respectively, and require the continuity of the tangential component of the E -field and of the normal component of the D -field.)