Suppose I have two plate electodes with a dielectric material between them with a permitivity of $\epsilon=10$. I now put a voltage V between them. What is the electric field in the dielectric region?
Well since the electrodes are plates we have simply:
$E = V/d$ which is independent of $\epsilon$.
On the other hand, my intuition tells me that this should depend on $\epsilon$. What is wrong with the argumentation above?
Best Answer
Yes. The voltage does depend on ε. Your argument is also correct. But you're missing the point of adding a dielectric. It reduces the total voltage of the system and helps to increase the capacitance. The electric field without a dielectric will be given by E = σ/ε, where σ denotes the surface charge density of the plates. When you introduce a dielectric between the plates (I assume here that you intend to fill the entire space between the two plates with the dielectric), the dielectric gets polarised as well, and thus produces an opposing field. In this case, the net electric field between the plates is given by E = (σ-σp)/ε, where σp stands for the surface charge density of the polarised dielectric. Here's a link that explains about polarization of the dielectric: (http://physics.bu.edu/~duffy/semester2/c08_dielectric.html)
σp can be given by σp = σ(1 - 1/k), where σ is the surface charge density of the plates, and k is the dielectric constant of the dielectric. Hope that helps.