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

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 h directly beneath each of these spheres is a fixed sphere with positive charge Q. (Use L for L, epsilon_0 for epsilon 0/ d for q, Q for Q, h for h, and W for W as needed.) Find the distance x when the rod is horizontal and balanced. 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

In a hydrogen atom in its ground state there is a nucleus of charge +e at the origin, surrounded by an electron density following eq.will be used. Substitution of (3) into Gauss' Law (1) then yields Poisson's Equation r2V(r) = ?? %(r) 0 (4) with integral solution [from Coulomb's Law - see Eq. (26) in Topic 1] V(r) = 1 40 ZZZ %(r0) r ?? r0 d3r 0; (5) the integration extending over the entire region containing charge. Notice that the principle of superposition applies to the electrostatic potential V(r) just as it does to the electrostatic eld vector E(r). Problem 9: Show that the integral expression given in Eq. (5) for the electrostatic potential satises Poisson's equation (4).

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