Saved Bookmarks
| 1. |
An infinite plane of uniform dielectric with permittivity epsilon is uniformly charged with extraneouschagre fo space density rho. The thicknessof the plate is equalto 2d. Find: (a) the magnitude of the electric field strength and the potential as functions ofdistancel fromthe middlepoint of the plane.(wherethe potentialis assumedto be equalto zero), having chosen teh x coriditnateaxis perpendicular to the plate, draw the approximate plotsof teh projection E_(x) (x) of the vector E and the potentail varphi (x), plotsfo the projection E_(x) (x) of the vector E adn the potential varphi (x), (b) the surface and space denstitesof the boundcharge. |
|
Answer» Solution :(a) div `vec(D) = (del D)/(del x) = rho` and `D = rho l` `E_(x) = (rho l)/(epsilon epsilon_(0)),l lt d` and `E_(x) = (rho d)/(epsilon_(0))` constantfor `l gt d`. `varphi (x) = - (rho l^(2))/(2epsilon epsilon_(0)), l lt d` and `varphi (x) = A - (rho ld)/(epsilon_(0)), l gt d` then`varphi (x) = (rho d)/(epsilon_(0)) (d - (d)/(2e) - t)`, by continuity. On the basic of obtained expressions`E_(x) (x)` and `varphi(x)` can be PLOTTED as SHOWN in fig of answersheet. (b) `rho' = -"div " vec(p) = -"div " (epsilon - 1) epsilon_(0) vec(E) = -rho ((epsilon - 1))/(epsilon)` `sigma' = P_(1n) - P_(2n)`, where `n` is the normal from 1 to 2. `P_(1n)`, (`vec(p_(2)) = 0` as 2 is vacumm.) `= (rho d - rho d//epsilon) = rho d (epsilon - 1)/(epsilon)` |
|