Problems Work on these problems with your Peer Team members. Determine analytic solutions before substituting any numerical values to find numerical solutions. Each problem is solved by use of either Equation (1), F ⇀ E = k ⁢ q 1 ⁢ q 2 r 2 ⁢ r ^ , or Equation (3), F ⇀ E q [ r ⇀ ] = k ⁢ q ⁢ ∑ n = 1 N q n r n 2 ⁢ r ^ n . These basic relationships should form the starting point of your solutions, although other basic relationships that you have encountered before, or perhaps have to look up, may also be needed to complete the solutions.

Problem 1 Two small silver spheres, each with a mass of 15.0 g, are separated by 0.50 m. Calculate the fraction of the electrons in one sphere that must be transferred to the other in order to produce an attractive force of 2.00 × 10 4 ⁢ N between the spheres. (The number of electrons per atom of silver is 47, and the number of atoms per gram is Avogadro's number divided by the molar mass of silver, 107.87 g/mol.)

Problem 2 Two tiny identical conducting spheres, initially carrying charges q 1 and q 2 , have a repulsive force between them of magnitude F i when separated by a distance r i . The two spheres are brought together, so that the total charge is equally shared between them. Then the spheres are separated by a distance of α ⁢ r i , and the force between them is found to be β ⁢ F i . Both α and β are pure numbers. Consider r i , F i , α ⁢ and ⁢ β to be known quantities. (a) Find the values of the initial charges q 1 and q 2 . (b) Are there any limits on the values of α and β in order that the solution makes sense?

Problem 3 Two point charges, q 1 = - 2.00 ⁢ μC ⁢ and ⁢ q 2 = 8.00 μC , are fixed in space a distance d = 10.0 cm apart, as shown in the figure below. A third point charge Q is placed in the vicinity of the fixed charges such that the electric force on Q is zero. What is the location of Q with respect to the fixed charges?

Problem 4 Three fixed charges lie on the corners of an equilateral triangle of side a = 15.0 cm , as shown in the figure below. Determine the electric force on a charge q = 2.00 μC placed at the center of the equilateral triangle. (The meaning of "center" of the triangle is implied by the figure.)