The electric field along the axis of a uniformly charged disk of radius R and total charge Q was calculated the given example. Show that the electric field at distances x that are large compared with R approaches that of a particle with charge Q = σπR2. Suggestion: First show that x/(x2 + R2)1/2 = (1 +R2/x2)-1/2 and use the binomial expansion (1 + δ)n ≈ 1 + nδ, when δ << 1. A disk of radius R has a uniform surface charge density o. Calculate the electric fieldat a point P that lies along the central perpendicular axis of the disk and a distance xfrom the center of the disk (Fig. 23.4).Figure 23.4 (Example 23.3)A uniformly charged disk ofdqradius R. The electric field at anaxial point Pis directed alongthe central axis, perpendicularto the plane of the disk.Rdr

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Principles of Physics: A Calculus-Based Text

5th Edition

ISBN:9781133104261

Author:Raymond A. Serway, John W. Jewett

Publisher:Raymond A. Serway, John W. Jewett

Chapter19: Electric Forces And Electric Fields

Section: Chapter Questions

Problem 57P: A solid conducting sphere of radius 2.00 cm has a charge 8.00 μC. A conducting spherical shell of...

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The electric field along the axis of a uniformly charged disk of radius R and total charge Q was calculated the given example. Show that the electric field at distances x that are large compared with R approaches that of a particle with charge Q = σπR². Suggestion: First show that x/(x² + R²)^1/2 = (1 +
R²/x²)^-1/2 and use the binomial expansion (1 + δ)ⁿ ≈ 1 + nδ, when δ << 1.

A disk of radius R has a uniform surface charge density o. Calculate the electric field
at a point P that lies along the central perpendicular axis of the disk and a distance x
from the center of the disk (Fig. 23.4).
Figure 23.4 (Example 23.3)
A uniformly charged disk of
dq
radius R. The electric field at an
axial point Pis directed along
the central axis, perpendicular
to the plane of the disk.
R
dr

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