SOLUTIONS: Solution set
Discussion Questions
4. Static electric buildup can be troublesome as, for example, in a photographic processing laboratory where film easily becomes charged (usually positively), attracting dust, and even creating sparks. To control the effect, there are static eliminators, one variety of which uses radioactive polonium-210. This material pours out a constant stream of positively charged alpha particles. How would that help?
12. Why are electrostatic phenomena, like sparks when you take off a sweater in the dark, more common in winter than in summer?
14. Figure Q14 shows a variation of the most widely used electrostatic generator, a device that carries the name of its inventor, Robert Van de Graaff. The two pulleys are covered with different materials so that when they are contacted by the motor-drive belt, the belt acquires a negative charge from the bottom pulley and a positive charge from the top one. In some research models, electrons are literally sprayed on the belt at the base. Figure out how the generator works and explain the crucial role of the hollow conductor dome. What, if anything, limits the amount of charge that can be built up on the dome? How would that compare to the case where the belt delivered the charge to the outside surface?
Problems
5. Two protons are fired directly at each other in a vacuum chamber. What is the force of repulsion at the instant they are 1.0 x 10**(-14) m apart?
9. An equilateral triangle with sides of 2.0 m is inscribed within a circle. A tiny charged sphere carrying (+10 micro C) is then fixed at each vertex, and one of -25 micro C is placed at the center of the circle. What is the net force acting on the central charge (magnitude and direction)?
16. Two charges of +4.0 nano C and -1.0 nano C are fixed to a baseline at a separation of 1.0 m. Where on the baseline should a third charge of + 2.0 nano C be placed if it is to experience zero net electric force?
25. A test-charge of +5.0 nano C placed at the origin of a coordinate system experiences a force of 4.0 x 10**(-6) N in the positive y-direction. What is the electric field at that location? Assume the mdeium is vacuum.
28. A small positively charged object is placed, at rest, in an uniform electric field. Write an equation giving its speed v after a time t in terms of its mass m and charge q.
29. Determine the magnitude and direction of an E-field if an electron placed in it, in vacuum, is to experience a force that will exactly cancel its weight at the Earth's surface.
37. Using Gauss's Law, determine the electric field in the air gap of a charged parallel plate capacitor. Use a cylindrical Gaussian surface with one endface embedded in the metal of one of the plates.
42. Three point-charges are placed at the corneres of an isosceles triangle. At the left and right, end points of the base are +1.0 micro C and +1.0 micro C, respectively, and at the vertex +3.0 micro C. The base of the triangle is 40 cm long and the altitude is 30 cm high. Find the E-field at the midpoint of the baseline.
43. Use Gauss's Law to determine a formula for the electric field outside of a long, uniformly charge cylinder of radius R with a positive surface charge density of sigma.