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Near the point A (Fig) lying on the bou...

Near the point `A` (Fig) lying on the boundary between glass and vacumm the electric field strength in vacumm is equal to `E_(0) = 10.0 V//m`, the angle between the vector `E` and `n`, as well as the surface density of the point charges at the point `A`.

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Let the field in the dielectric be `vec(E)` making an angle `alpha` with `vec(n)`. Then we have the boundary conditions,
`E_(0) cos alpha_(0) = epsilon E cos alpha` and `E_(0) sin c_(0) E sin alpha`
So `E = E_(0) sqrt(sin^(2) alpha_(0) + (1)/(epsilon^(2)) cos^(2) alpha_(0))` and `tan alpha = epsilon tan alpha_(0)`
In the dielectric the normal component of the induction vector is
`D_(n) = epsilon_(0) epsilon E_(n) = epsilon_(0) epsilon E cos alpha = epsilon_(0) E_(0) cos alpha_(0)`
`sigma' = P_(n) = D_(n) - epsilon_(0) epsilon_(n) = (1 - (1)/(epsilon)) epsilon_(0) cos alpha_(0)`
`sigma' = (epsilon - 1)/(epsilon) epsilon_(0) E_(0) cos alpha_(0)`
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