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PP(a)(b)

Question

Suppose you design an apparatus in which a uniformly charged disk of radius R is to produce an electric field. The field magnitude is most important along the central perpendicular axis of the disk, at a point P at distance 3.80R from the disk (see Figure (a)). Cost analysis suggests that you switch to a ring of the same outer radius R but with inner radius R/3.80 (see Figure (b)). Assume that the ring will have the same surface charge density as the original disk. If you switch to the ring, by what part will you decrease the electric field magnitude at P?

 

P
P
(a)
(b)
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P P (a) (b)

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check_circleAnswer
Step 1

Given:

Distance of point P is, z 3.8R
Outer radius,R
R
Inner radius of ring, r =
3.8
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Distance of point P is, z 3.8R Outer radius,R R Inner radius of ring, r = 3.8

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Step 2

Let the inner radius of the disc is r and the outer radius is R. The electric field at point P at distance z is,

σds
Z
1
4Te,zR z+ R°
ing
Where
a Areal charge density
(Rde)
σζ
Ering4TE
3
R
1
σζ
R
1
1
σ
Fing
26 zR2
1
1
σ
Ering
26 zR 2 +1
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σds Z 1 4Te,zR z+ R° ing Where a Areal charge density (Rde) σζ Ering4TE 3 R 1 σζ R 1 1 σ Fing 26 zR2 1 1 σ Ering 26 zR 2 +1

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Step 3

For disk, r=0

...

1
1
στ
Εj
2ε
1
1
σζ
Εμ
2ε,1 V
Vz +R
.2
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1 1 στ Εj 2ε 1 1 σζ Εμ 2ε,1 V Vz +R .2

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Science

Physics

Electromagnetic Induction

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