A particle with charge q on the negative x axis and a second particle with charge 2q on the positive x axis are each a distance d from the origin. Where should a third particle with charge 3q be placed so that the magnitude of the electric field at the origin is zero?

Show that the maximum magnitude Emax of the electric field along the axis of a uniformly charged ring occurs at x=a/2 (see Fig. 23.3) and has the value Q/(630a2). Figure 23.3 (Example 23.2) A uniformly charged ring of radius c. (a) The field at P on the x axis due to an element of charge dq. (b) The perpendicular component of the field at P due to segment 1 is canceled by the perpendicular component due to segment 2.

Two solid spheres, both of radius 5 cm, carry identical total charges of 2 C. Sphere A is a good conductor. Sphere B is an insulator, and its charge is distributed uniformly throughout its volume. (i) How do the magnitudes of the electric fields they separately create at a radial distance of 6 cm compare? (a) EA EB = 0 (b) EA EB 0 (c) EA = EB 0 (d) 0 EA EB (e) 0 = EA EB (ii) How do the magnitudes of the electric fields they separately create at radius 4 cm compare? Choose from the same possibilities as in part (i).

A 1.75-nC charged particle located at the origin is separated by a distance of 0.0825 m from a 2.88-nC charged particle located farther along the positive x axis. If the 1.75-nC particle is kept fixed at the origin, where along the positive x axis should the 2.88-nC particle be located so that the magnitude of the electrostatic force it experiences is twice as great as it was in Problem 27?

Point charges of 31.0 µC and 45.0 µC are placed 0.500 m apart. (a) At what point along the line connecting them is the electric field zero? |m (from the smaller charge) (b) What is the magnitude and direction of the net electric field halfway between them? magnitude N/C direction toward the smaller charge

In the classical model of an atom, the electron revolves around the proton with a radius of r = 0.53x1010 m. The magnitude of the charge of the electron and proton is e=1.6x101c. (a) What is the magnitude of the electric force between the proton and the electron? (b) What is the magnitude of the electric field due to the proton at r? -27, (c) Given that the mass of the electron is m, =9.1x10"kg and the mass of the proton is m, =1.7x10 "kg, what is ratio of the magnitudes of the electrical and gravitational force between electron and proton? Does the result depend on the distance between the proton and the electron? (d) In light of your calculation in (b), explain why electrical forces do not influence the motion of planets.