Calculate dielectric constants at an angle

  • #1

Homework Statement



For an application you require a thin wafer of dielectric with dielectric constant = 12 perpendicular to the wafer. You have available a tetragonal crystal of dielectric ceramic with relative dielectric constants εx = εy = 18. and εz = 10. At what angle to the z axis will you cut the wafer? (this is the angle between the z-axis and the normal to the plane of the wafer).

Homework Equations



D=E_ij*ε_ij*ε_0 (in vector form)

The Attempt at a Solution



I tried to break it down into the components like I would do in a 2D case where D1=E1*ε11*ε0 (repeat for 2 and 3) where E1=Ecosθ and E2=sinθ. Now I do not know what E3 should be. I am sure it is not tanθ.....Maybe I am wrong overall. If anyone can help me out that would be great.
 

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