Chapter 22, Problem 024 Your answer is partially correct. Try again. A thin nonc

Question

Chapter 22, Problem 024 Your answer is partially correct. Try again. A thin nonconducting rod with a uniform distribution of positive charge 2 is bent into a circle of radius R (see the figure). The central perpendicular axis through the ring is a z axis, with the origin at the center of the ring. What is the magnitude of the electric field due to the rod at (a) z 0 and (b) z oo? (c) In terms of R, at what positive value of z is that magnitude maximum? (d) If R 2.25 cm and Q 4.20 HC, what is the maximum magnitude? (a) Number Unit TN/C or V/m Unit T NIC or V/m (b) Number (c) Numbe Units Units (d) Numbe click if you would like to show work for this question Open Show Work

Explanation / Answer

Obtained by integration:
E = kQz/(r^2+z^2)^(3/2)
Set the first derivative of this function to zero.
Using the product rule for differentiation find:
dE/dz = kQ[ (r^2+z^2)^-(3/2) - 3z^2(r^2+z^2)^-(5/2)] = 0
multiply both sides of this equation by (r^2+z^2)^(5/2) and divide both by kQ:
dE/dz = (r^2+z^2) - 3z^2 = 0
r^2 +z^2 -3z^2 = 0
r^2 - 2z^2 = 0
r^2 = 2z^2
=>z = (+/-) r/sqrt(2)
Z=0.0225/2=0.016
Pop z,r, and Q into E = kQz/(r^2+z^2)^(3/2)

E= 28.74 * 10^6

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