- #1

PhysicsRock

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- Homework Statement
- Consider a plate capacitor with distance ##d = 3 \, \text{mm}## and an area of ##A = 100 \, \text{cm}^2##. The distance is divided into segments of equal length ##a = 1 \, \text{mm}##. A dielectric is insertet between ##x = a## and ##x = 2a## that has a relative permittivity of ##\varepsilon_r = 2.0##. The potential difference between the plates is ##U_0 = 30 \, \text{V}##. Calculate the magnitude ##E(x)## of the electric field inside the capacitor.

Addition: Since not explicitly given otherwise, I assume the rest of the capacitor is filled with a vacuum.

- Relevant Equations
- ##\frac{E_\text{dielec.}}{E_\text{vac}} = \frac{1}{\varepsilon_r}##

##E = \frac{U}{d}##.

My attempt would be to calculate the electric fields of the vacuum and dielectric part seperately and then use superpositioning to obtain the full solution. However, I don't see an ##x##-dependency coming along that path. The assignment suggests that there must be one though. Unfortunately, this type of contraption has not been covered in lectures so far, only for the case that the dielectric coveres the entire area, which I don't think is fulfilled here. Help is appreciated.