(1) Two protons in a molecule are separated by a distance of 3.8´10^-10m. Find the electrostatic force exerted by one proton on the other.

(2) A 6.7mC charge is located 5m from a -8.4mC charge.  Find the electrostatic force exerted by one on the other.

(3) Two fixed charges, +1.0´10^-6C and -3.0´10⁶C, are 10cm apart. (a) Where may a third charge be located so that no force acts on it? (b) Is the equilibrium of this third charge stable or unstable?

(4) Each of two small spheres is charged positively, the combined charge being 5.0´10^-5C.  If each sphere is repelled from the other by a force of 1.0N when the spheres are 2.0m apart, how is the total charge distributed between the spheres?

(5) A certain charge Q is to be divided into two parts, q and Q-q. What is the relationship of Q to q if the two parts, placed a given distance apart, are to have a maximum Coulomb repulsion?

(6) A 1.3mC charge is located on the x-axis at x=-0.5m, 3.2mC charge is located on the x-axis at x=1.5m, and 2.5mC charge is located at the origin.  Find the net force on the 2.5mC charge.

(7) A point charge q₁= -4.3mC is located on the y-axis at y=0.18m, a charge q₂=1.6mC is located at the origin, and a charge q₃=3.7mC is located on the x-axis at x= -0.18m. Find the resultant force on the charge q₁.

(8) Three point charges of 2mC, 7mC, and –4mC are located at the corners of an equilateral triangle as shown in the figure 2.9. Calculate the net electric force on 7mC charge.

Figure 2.9

(9) Two free point charges +q and +4q are a distance 1cm apart.  A third charge is so placed that the entire system is in equilibrium.  Find the location, magnitude and sign of the third charge.  Is the equilibrium stable?

(10) Four point charges are situated at the corners of a square of sides a as shown in the figure 2.10.  Find the resultant force on the positive charge +q.

Figure 2.10

(11) Three point charges lie along the y-axis.  A charge q₁=-9mC is at y=6.0m, and a charge q₂=-8mC is at y=-4.0m. Where must a third positive charge, q₃, be placed such that the resultant force on it is zero?

(12) A charge q₁ of +3.4mC is located at x=+2m, y=+2m and a second charge q₂=+2.7mC is located at x=-4m, y=-4m. Where must a third charge (q₃>0) be placed such that the resultant force on q₃ will be zero?

(13) Two similar conducting balls of mass m are hung from silk threads of length l and carry similar charges q as shown in the figure 2.11.  Assume that q is so small that tanq can be replaced by sinq.  Show that

where x is the separation between the balls (b) If l=120cm, m=10g and x=5cm, what is q?