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 $3\mathrm{.}40R$ 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 $\frac{R}{3\mathrm{.}40}($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 $P?$

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