Internal E-field of dielectric cylinder immersed in static E-field

[grmitch]

I am having trouble with a homework problem assigned by my physics professor. An infinitely long cylinder of radius a and relative dielectric constant Er is immersed in a static electric field E=Eox where x is supposed to denote a unit vector in the x direction. The cylinder is alligned on the z direction. The question is how do I find the electric field inside of the cylinder. I thought about using transmission and reflection coefficients to determine how much of the field would be transmitted into the cylinder but these really only apply to incident wave equations. I am at a total loss here. Any input would help a lot.

Thanks in advance for anyone's input. This seems like it should be an easy problem but I must be failing to grasp some fundamental concept.

Jim

 

[grey_earl]

You need the surface conditions, i.e. which part (horizontal or vertical with respect to the surface) of the electric field $$\vec{E}$$ and the displacement field $$\vec{D}$$ are constant across the surface and which change.

 

[grmitch]

Th E-field is in the x-direction and the cylinder's axis is alligned along the z-axis. Therefore the E-field is normal to the cylinder. There is no tangential component to the E-field. The field is static everywhere, i.e. not propagating.

 

[grmitch]

Also the cylinder is infinitely long

 

[grey_earl]

Ok, but what I meant was:
from the general theory of electromagnetism, is the normal component of the $$\vec{E}$$ field continuous across a surface or does it jump? And the parallel component? And what about the $$\vec{D}$$ field? If they jump, they do so by a well-defined amount, namely the quotient of the two dielectric constants before and behind the surface. Look it up in your course notes, this is what you need to solve the problem.

(I mean this: http://en.wikipedia.org/wiki/Interface_conditions_for_electromagnetic_fields, but your professor should have it explained it a bit more)

 

[grmitch]

No the fields do not jump. The normal of the D-field and tangential components of the E field are continuous across the boundary of the cylinder

 

[grey_earl]

Right. And what about the tangential of the D field and the normal component of the E field?