Chapter 22, Problem 037 Your answer is partially correct. Try again. Suppose you

Question

Chapter 22, Problem 037 Your answer is partially correct. Try again. 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 2.20R 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/2.20 (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? Number T3.3 Units No units the tolerance is +/-5% LINK TO TEXT LINK TO SAMPLE PROBLEM LINK TO SAMPLE PROBLEM VIDEO MINI-LECTURE

Explanation / Answer

    

The decrease in magnitude at point P is simply the magnitude of the field that WOULD have been produced by the white area on the second image.

For (a), E = k2[1 - z / (z² + R²)]
For (b), E' = k2[1 - z / (z² + (R/4.10)²)] for the "missing" area
so
E' / E = [1 - z / (z² + (R/4.10)²)] / [1 - z / (z² + R²)]
When z = 2.20 R,
E' / E = [1 - 2.20R / ((2.20R)² + (R/2.20)²)] / [1 - 2.20R / ((2.20R)² + R²)]
E' / E = [1 - 2.20R / R5.04] / [1 - 2.20R / R5.84]
E' / E = 0.020 / .0896= .223
which represents a reduction of 22.3%

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