Suppose you design an apparatus in which a uniformly charged disk of radius R is

Question

Suppose you design an apparatus in which a uniformly charged disk of radiusRis to produce an electric field. The field magnitude is most important along the central perpendicular axis of the disk, at a pointPat distance1.20Rfrom the disk (Fig. a). Cost analysis suggests that you switch to a ring of the same outer radiusRbut with inner radiusR/2.00 (Fig. b). Assume that the ring will have the same surface charge density as the original disk. If you switch to the ring, by what percentage will you decrease the electric field magnitude atP?
%

Explanation / Answer

1) write an equation to express E at P as a function of R and theta on the disk. 2) integrate from 0 to R, and from 0 to 2pi. Make this your denominator. Repeat step 2, integrating from 0.5R to R. Make this your numerator. cancel any like terms in numerator and denominator. Multiply by 100%. Surface charge equation: E_vector = Integral of [ rho dS / (4 pi epsilon r^2) ] a_vector, where: 1) rho is charge density (this will cancel in your case) 2) dS the area you are integrating. In your case, dS is something like 2 pi dr dTheta. 3) epsilon = permitivitiy of free space. (this will cancel in your case) 4) a_vector: a unit vector pointing in the direction of r. 5) r is a vector from some "field point" P, to the point on the disk you are presently integrating. Note: R and a_vector change as you integrate.

Related Questions

Navigate

• Browse (All)
• Browse S
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.