In the configuration below the electric field intensity in m

In the configuration below, the electric field intensity in medium (1) has a magnitude E_0 and is directed at 45 degree degrees to the normal as shown. A surface charge density exists at the interface between the two dielectrics. What must be the surface charge density so that the electric field intensity in medium (2) is parallel to the interface. Give magnitude and polarity of the surface charge density.

Solution

at boundary

DN1 - DN2 = Ps (charge density)

e1*EN1 - e2*EN2 = Ps

as per the given data E2 = parallel to the surface there by E2N = 0

from the above consideration

Ps = -e2*EN2 = -e2*Eo*cos(45) = -e2*0.707*Eo