AAPT UNITEDSTATES PHYSICS TEAM AIP 2007 A3.A volume V of fluid with uniform charge density p is sprayed into a room,forming spherical drops.As they float around the room,the drops may break apart into smaller drops or coalesce into larger ones.Suppose that all of the drops have radius R.Ignore inter-drop forces and assume that VR. (10 pts)a.Calculate the electrostatic potential energy of a single drop.(Hint:suppose the sphere has radius r.How much work is required to increase the radius by dr?). (4 pts)b.What is the total electrostatic energy of the drops? Your answer to(b)should indicate that the total energy increases with R.In the absence of surface tension,then,the fluid would break apart into infinitesimally small drops.Suppose, however,that the fluid has a surface tension y.(This value is the potential energy per unit surface area,and is positive.) (4 pts)c.What is the total energy of the drops due to surface tension? (7 pts)d.What is the equilibrium radius of the drops? Copyright 2007,American Association of Physics TeachersCopyright © 2007, American Association of Physics Teachers A3. A volume Vf of fluid with uniform charge density ρ is sprayed into a room, forming spherical drops. As they float around the room, the drops may break apart into smaller drops or coalesce into larger ones. Suppose that all of the drops have radius R. Ignore inter-drop forces and assume that 3 . V R f  (10 pts) a. Calculate the electrostatic potential energy of a single drop. (Hint: suppose the sphere has radius r. How much work is required to increase the radius by dr?). (4 pts) b. What is the total electrostatic energy of the drops? Your answer to (b) should indicate that the total energy increases with R. In the absence of surface tension, then, the fluid would break apart into infinitesimally small drops. Suppose, however, that the fluid has a surface tension γ . (This value is the potential energy per unit surface area, and is positive.) (4 pts) c. What is the total energy of the drops due to surface tension? (7 pts) d. What is the equilibrium radius of the drops?