1.

Under certain condinates the polarrization of an infinite uncharged dielectric plate , takes the form `P = P_(0)` is a vector perpendicular to the plate, `x` is the distance from the of the electric field inside the plate and the potentail difference between its surface.

Answer» Since there are no free extraneous chagres anywhere
`di v vec(D) = (del D)/(del x) = 0` or, `D_(x)` = constant
But `D_(x) = 0` at `oo`, so `D_(x) = 0`, every where.
Thus, `vec(E) = - (vec(P_(0)))/(epsilon_(0)) (1 - (x^(2))/(d^(2)))` or `E_(x) = (P_(0))/(epsilon_(0)) (1 - (x^(2))/(d^(2)))`
So, `varphi = (P_(0)x)/(epsilon_(0)) - (P_(0) x^(3))/(3 epsilon_(0) d^(2)) +` constant
Hence, `varphi(+d) - varphi(-d) = (2P_(0))/(epsilon_(0)) - (2 P_(0) d^(3))/(3 d^(2) epsilon_(0)) = (4 P_(0) d)/(3 epsilon_(0))`


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