Each of the charged objects described in parts (a)-(c) lie in the xy-plane and are centered on the origin. In each part: (i) Calculate the electric field at a point z along the z-axis. (ii) Discuss the asymptotic behavior of your answer for large z (i.e., much larger than the size of the object). Is it as you would expect? Explain. (a) A circular loop of radius R that carries a uniform line charge 2. (b) A flat circular disk of radius R that carries a uniform surface charge o.

Each of the charged objects described in parts (a)-(c) lie in the xy-plane and are centered on the origin. In each part: (i) Calculate the electric field at a point z along the z-axis. (ii) Discuss the asymptotic behavior of your answer for large z (i.e., much larger than the size of the object). Is it as you would expect? Explain. (a) A circular loop of radius R that carries a uniform line charge 2. (b) A flat circular disk of radius R that carries a uniform surface charge o.

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

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Concept explainers

Electric Charges and Fields

One of the fundamental properties is the electromagnetic property. Charge cannot be destroyed by any process and this contributes formally to the law of charge conservation.

Question

### Problem Description

Each of the charged objects described in parts (a)-(c) lie in the xy-plane and are centered on the origin. For each part, perform the following tasks:

(i) **Calculate the electric field** at a point \( z \) along the z-axis.

(ii) **Discuss the asymptotic behavior** of your answer for large \( z \) (i.e., much larger than the size of the object). Is it as you would expect? Explain.

### Charged Objects

(a) **A circular loop** of radius \( R \) that carries a uniform line charge \( \lambda \).

(b) **A flat circular disk** of radius \( R \) that carries a uniform surface charge \( \sigma \).

(c) **A flat circular disk** of radius \( R \) that carries a nonuniform, but cylindrically symmetric, surface charge given by:

\[
\sigma(s) = \sigma_0[1 - (3s/2R)]
\]

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Step 2: (i) Calculate electric field at a point z along z axis:

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Step 3: (ii) Behavior for large z:

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Step 4: b) Determine the given data:

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Step 5: (i) Calculate electric field at a point z along z axis:

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Step 6: (ii) Behavior for large z:

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