# Homework Help: Calculate E - capacitor question

1. Aug 20, 2011

### blueyellow

1. The problem statement, all variables and given/known data

Consider a parallel plate capacitor with square plates of side L and distance d<<L apart. The bottom plate lies on the x-y plane, and the distance d is parallel to z. A block of dieletric material can completely fill the space between the plates.

Consider the dieletric to be composed of two materials glued together, material 1 with dieletric constant epsilon1 and dimensions 0.6L*L*d (in x, y and z directions, respectively) and material 2 with constant epsilon2 and dimensions 0.4L*L*d. The dielectric is free to move as a single block without friction along the x axis, parallel to the plates inside the capacitor, and it can also move outside the capacitor. Let us define as x the distance between the dielectric and the edge of the plates, and we can neglect the electric field outside the plates. Considering that the potential difference between two points a and b is delta V= integral from a to b of E.dl, and that D=epsilon0*epsilon(subscript r)*E, where epsilon(subscript r) is the dielectric constant, calculate the value of the electric field E and of the electric displacement field D in the region between the plates, for the three possible regions where the space is occupied by the material 1, the one with material 2, and the vacuum.

2. Relevant equations

2. Aug 20, 2011

### blueyellow

attempt at solution:

E=q/(epsilon0 *A)

E=deltaV/d

= integral from a to b of E.dl /d