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 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 4.40R? 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 R/4.40 (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?

Explanation / Answer

Electric field on the axis of the disc is given by
E = 2*pi*k*sigma[1 - x/sqroot(x^2 + R^2)]
k = coulomb's constant
sigma = charge density
x = 4.40 R

so E in case 1, E1 = 2*pi*k*sigma[1 - 4.4/4.5122] = 2*pi*k*sigma*0.0248671
and E2 = Field due to whole disc - field due to missing part
E2 = 2*pi*k*sigma*[1 - 4.4/4.5122 - 1 + 4.4R/sqroot((4.4R)^2 + (R/4.4)^2)] = 2*pi*k*sigma(4.4/4.405 - 4.4/4.5122) = 2*pi*k*sigma*0.02353

E1 - E2 = 2*pi*k*sigma*0.0013325
(E1 - E2)/E1 = 0.0013325/0.0248671 = 0.053585 = 5.3585 percent

Related Questions

Navigate

• Browse (All)
• Browse S
• Subjects

---

---

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