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A round dielectric disc of radius R and thicknessdis statically polarizedso thatit gainsthe uniform polarzationP. Withthe vector Plyingin theplaneof the disc. Findthe strength E ofthe electricfield at the centre of the disc if d lt lt R. |
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Answer» <P> Solution :Because there is a discontinuity in polarization at the boundary of the dielectric disc, a bound surface charge appears, which is the SOURCE of the electric field inside and outside the disc.We have for the electric field at the origin. `vec(E) = -int (sigma dS)/(4pi epsilon_(0) r^(3)) vec(r)`, where `vec(r )` = radius vector to the origin form the element`dS`. `sigma' = P_(n) = P cos theta` on the CURVED surface `(P_(n) = 0` on the flat surface.) Here `theta` = angle between `vec(r )` and `vec(P)` By symmetry, `vec(E)` will be parallel to `vec(P)`. Thus `E = -int_(0)^(2x) (P cos theta R d theta cos theta)/(4pi epsilon_(0) R^(2)) .d` where, `r = R` it `d lt lt R`. So, `E = - (PD)/(4 epsilon_(0) R)` and `vec(E) = - (vecP d)/(4epsilon_(0) R)` 
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