Consider two identical conducting spheres whose surfaces are separated by a small distance. One sphere is given a large net positive charge while the other is given a small net positive charge. It is found that the force between them is attractive even though both spheres have net charges of the same sign. Explain how this is possible.

Three identical conducting spheres denoted as X, Y, and Z are separated in space. They have initial net charges of −2Q, −3Q, and 5Q, respectively. Sphere Z is touched to X and separated, then touched to Y and separated. Upon reaching electrostatic equilibrium, what is the final net charge of Y?

Three charged marbles are glued to a nonconducting surface and are placed in the diagram as shown. The charges of each marble are q1 = 6.20 µC, q2 = 1.43 µC, and q3 = −2.01 µC. Marble q1 is a distance r1 = 3.00 cm to the left of the marble q2, while marble q3 is a distance r3 = 2.00 cm to the right of the marble q2. Calculate the magnitude of the electric field a distance r' = 1.00 cm to the left of the center marble.N/C Another marble is placed 1 cm to the left of the middle marble. If this new marble has a charge of  3.62 µC, calculate the magnitude and direction of the force on it.

Two identical metal blocks resting on a smooth horizontal surface are connected by a lightweight spring having a spring constant k = 0.2 N/m, as shown in the figure. The length of the spring before it is stretched is L0 = 10 cm. A total charge Q is carefully applied to the block, which is assumed to be a point charge. Because the blocks are given an electric charge, the spring is stretched so that its length becomes L = 10.2 cm. Find Q!

A 8-g charged plastic sphere charged to 75 µC is on top of a plastic spring with spring constant k = 400 N/m, which has a relaxed length of 10 cm. You then place another charged object 1 cm above (not touching) the sphere. Now, the spring is 9.5 cm long. Find the charge on the new second object.

Two spherical, hollow conductors are concentrically nested as shown in the cross-sectional diagram below and electrically isolated from each other. A net charge of -3 nC is divided between the conductors, with a total of -12 nC on the inner conductor and +9 nC on the outer one. The charges are, of course, free to move between the surfaces within each shell but cannot move from one shell to the other. The inner conductor has an inner radius of a=2 cm, outer radius of b=3 cm. The outer conductor has an inner radius of c=6 cm, an outer radius of d=8 cm. a (a) In equilibrium, all of the excess charge is found on the surfaces. Why is there no charge between a and b, nor between c and d? (b) Determine the net charge on each surface (ie how much charge is there at r = a, at r = b, at r = c and at r= = d). (c) Is the charge on the outer surface equal to the net charge on the outer container, the net charge of the system, or some other amount? Explain briefly. (d) Find the surface charge…

Problem 6:   A conducting sphere of radius r1 = 0.18 m has a total charge of Q = 1.4 μC. A second uncharged conducting sphere of radius r2 = 0.42 m is then connected to the first by a thin conducting wire. The spheres are separated by a very large distance compared to their size. What is the total charge on sphere two, Q2 In coulombs

(a) Two point charges totaling 8.50 μC exert a repulsive force of 0.200 N on one another when separated by 0.479 m. What is the charge (in µC) on each? smallest charge 1.0 X UC x uc largest charge 8.39 (b) What is the charge (in uc) on each if the force is attractive? smallest charge PC largest charge PC Additional Materials Reading