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Physics / Introduction to Electrodynamics 4 / Chapter 4 / Problem 34P

Introduction to Electrodynamics | 4th Edition | ISBN: 9780321856562 | Authors: David J. Griffiths

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Solved: The space between the plates of a parallel-plate

Chapter 4, Problem 34P

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QUESTION:

Problem 34P

The space between the plates of a parallel-plate capacitor is filled with dielectric material whose dielectric constant varies linearly from 1 at the bottom plate (x = 0) to 2 at the top plate (x = d). The capacitor is connected to a battery of voltage V. Find all the bound charge, and check that the total is zero.

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QUESTION:

Problem 34P

The space between the plates of a parallel-plate capacitor is filled with dielectric material whose dielectric constant varies linearly from 1 at the bottom plate (x = 0) to 2 at the top plate (x = d). The capacitor is connected to a battery of voltage V. Find all the bound charge, and check that the total is zero.

ANSWER:

Solution

Step 1 of 4

We have to find all the boundary charge and check that the total is zero. The voltage is connected to the bottom plate, so the electric field points in the x direction. The charge density is positive in the lower plate and negative on the upper plate.

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