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A point charge q si located on the plane dividingvacumm and infiniteuniformistropicdielectricwith permittivity eposilon. Find the moduliof the vectors D and Eas well as the potentail varphi as funtions of distancer fromthe charge q. |
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Answer» <P> SOLUTION :`E_(p) = (Q vec(r_(1)))/(4pi epsilon_(0) r_(1)^(3)) + (q vec(r_(2)))/(4pi r_(2)^(3) epsilon_(0)), P` in 1`E_(R ) = (q" vec(r_(1)))/(4pi epsilon_(0) r_(1)^(3)), P` in 2 where`q'' = (2q)/(epsilon + 1) , q' = q'' - q` In the limit `vec(l) rarr 0` `vec(E_(p)) = ((q + q') vec(r))/(4pi epsilon_(0) r^(3)) = (q vec(r))/(2pi epsilon_(0) (l + epsilon) r^(3))`, in either part, Thus `E_(p)= (q)/(2pi epsilon_(0) (l + epsilon) r^(2))` `varphi = (q)/(2pi epsilon_(0)(l + epsilon) r)` `D = (q)/(2pi epsilon_(0)(l + epsilon) r^(2)) xx {{:("1 in vacum"),(epsilon" in dielectric"):}` 
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