Figure 22-25 shows a long, nonconducting, massless rod of length L , pivoted at

Question

Figure 22-25 shows a long, nonconducting, massless rod of length L, pivoted at its center and balanced with a weight W at a distance x from the left end. At the left and right ends of the rod are attached small conducting spheres with positive charges q and 2q, respectively. A distance hdirectly beneath each of these spheres is a fixed sphere with positive charge Q. (Use L for L, epsilon_0 for 0, q for q, Q for Q, h for h, and W forW as needed.)

(a) Find the distance x when the rod is horizontal and balanced.

The answer is not (L/2)*(1+(k*q*Q)/(W*h^2))

(b) What value should h have so that the rod exerts no vertical force on the bearing when the rod is horizontal and balanced?

Explanation / Answer

(a)
Balance the torques. Let the point of rotation be the left end. Since the rod is horizontal, the distance between Q and 2q is h. Set the clockwise torques equal to the counterclockwise torques:
W*x = (k*Q*2q*L)/h^2

x = (k*Q*2q*L)/(W*h^2)

(b)
Balance the vertical forces
k*Q*q/h^2 + k*Q*2q/h^2 = W
h = sqrt[3*k*Q*q/W]

Related Questions

Navigate

• Browse (All)
• Browse F
• Subjects

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