Yes that's what I meant slight typo! However, the way I defined E was already as the normal component. Thanks for your help I've solved this now, you're right it was a case of solving for sigma by including it in both terms.
So yes just to clarify, I think the two fields I've calculated are correct. However, I don't really understand why the question is asking for the induced surface charge in this way when you already know it from the dotting the polarisation with the unit normal. Am I confusing some of the...
Homework Statement
A point charge Q is placed at a perpendicular distance a from an infinite planar LIH (linear, isotropic, homogeneous) dielectric of relative permittivity ε. By considering the normal component of the electric field at an arbitrary point just inside the dielectric to be the...