Electric field inside dielectric cylinder

[jmz34]

A dielectric cylinder of radius 'a' and permittivity 'e' is placed in a uniform field Eo with the direction of field perpendicular to the axis of the cylinder, find the E field (Ei) inside the cylinder. I CAN DO THIS PART OF THE QUESTION FINE. It turns out that:

Ein=2Eo/(1+e)

Next, consider the situation where the cylinder is tipped so that its axis makes an angle phi to Eo, find a new expression for Ein.

I know I'm supposed to use the continuity conditions that D-perpendicular and E-parallel are continuous at the interface, but I'm confused as to how to go about doing this. I've come up with the equations Eosin(theta1)=Eintsin(theta2) where I think theta1=90-phi.

Thanks in advance.

 

[Born2bwire]

All you need to do is decompose the field into components that are now perpendicular and parallel to the axis of the cylinder. Once you have that, you can apply the same analysis as before on these two parts and treat them independently. So for the perpendicular part, if the axis was along z, then the perpendicular would be in the \rho direction. So that would be cos(\theta) since it should maximize when \theta was zero. Likewise, the parallel part should be zero when \theta is zero so it should be something like sin(\theta). Here, \theta is the angle between the z-axis and the axis of the cylinder.