The electric field along the axis of a uniformly charged disk of radius R and total charge Q is given below. E, = 2xk, o ( + R)/2 Show that the electric field at distances x that are large compared with R approaches that of a partide with charge Q = GTR2. Suggestion: First show that x/(x + R2)1/2 = (1 + R2/x1/2 and use the binomial expansion (1 + 8)n= 1+ nổ when 8 « 1. (Do this on paper. Your instructor may ask you to turn in this work.)

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The electric field along the axis of a uniformly charged disk of radius R and total charge Q is given below.
E = 2zk, o
1-
(2 + R?)1/2
Show that the electric field at distances x that are large compared with R approaches that of a particle with charge O = aTR2. Suggestion: First show that x/(x2 + R2)1/2 = (1+
R2/x2)-1/2, and use the binomial expansion (1 + 8)" 1 + nổ when 8 « 1. (Do this on paper, Your instructor may ask you to turn in this work.)
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Transcribed Image Text:The electric field along the axis of a uniformly charged disk of radius R and total charge Q is given below. E = 2zk, o 1- (2 + R?)1/2 Show that the electric field at distances x that are large compared with R approaches that of a particle with charge O = aTR2. Suggestion: First show that x/(x2 + R2)1/2 = (1+ R2/x2)-1/2, and use the binomial expansion (1 + 8)" 1 + nổ when 8 « 1. (Do this on paper, Your instructor may ask you to turn in this work.) Filters Add a caption...
Expert Solution
Step 1

Given:

The charge density of the disk is σ.

The charge on the disk is Q=σπR2.

The electric field due to disk is given below.

Ex=2πkeσ1-xx2+R21/2                                                                ...(1)

 

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