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Physics / Introduction to Electrodynamics 4 / Chapter 2 / Problem 45P

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

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Find the electric field at a height z above the center of

Chapter 2, Problem 45P

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QUESTION:

Problem 45P

Find the electric field at a height z above the center of a square sheet (side a) carrying a uniform surface charge σ. Check your result for the limiting cases a→∞and z ≫a.

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QUESTION:

Problem 45P

Find the electric field at a height z above the center of a square sheet (side a) carrying a uniform surface charge σ. Check your result for the limiting cases a→∞and z ≫a.

ANSWER:

Step 1 of 3

We have to find the electric field at a height $z$ above the center of a square sheet (side $a$ ) carrying a uniform surface charge $\sigma{}$ .

The field at height $z$ above the center of a square loop of side $a$ is given by

Now, here $\lambda{}\rightarrow{}\sigma{}\frac{da}{2}$ and we integrate over the side $a$ from $0$ to $\bar{a}$

The electric field $\vec{E}$ is given by

Let

Therefore, the electric field at a height z above the center of a square sheet (side a) carrying a uniform surface charge is

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