As.rFall 12 PHY 122 Homework Solutions #1

Transcription

1 As.rFall 12 PHY 122 Homework Solutions #1 Chapter 21 Question 4 A positively charged rod is brought close to a neutral piece of paper, which it attracts. Draw a diagram showing the separation of charge in the paper, and explain why attraction occurs. Solution Fig The neutral piece of paper is composed of atoms and molecules which consist of positively charged nuclei surrounded by negatively charged electrons. The introduction of a positively charged rod will attract the electrons while maintaining their bond within the atom or molecule. Since the negatively charged electrons are closer than the positively charged nuclei the paper will be feel a stronger Coulombic attractive force than a Coulombic repulsive force. Chapter 21 Question 6 Contrast the net charge on a conductor to the free charges in the conductor. Solution The net charge is difference between the total positive and negative charge on the conductor. The free charges are the sum of all the total electrons that free to move within the conductor. Thus it is possible for a conductor to have free charges of electrons but a net charge of zero.

2 Chapter 21 Question 7 Figures 21 7 and 21 8 show how a charged rod placed near an uncharged metal object can attract (or repel) electrons. There are a great many electrons in the metal, yet only some of them move as shown. Why not all of them? Solution Fig 21-7 Fig 21-8 In Figure 21-7, electrons will move until the attractive force on the remaining conduction electrons due to the incoming charged rod is balanced by the repulsive force from electrons that have already gathered at the left end of the neutral rod. In Figure 21-8, conduction electrons will be repelled by the incoming rod and will leave the stationary rod through the ground connection until the repulsive force on the remaining conduction electrons due to the incoming charged rod is balanced by the attractive force from the net positive charge on the stationary rod. Chapter 21 Question 10 We are not normally aware of the gravitational or electric force between two ordinary objects. What is the reason in each case? Give an example where we are aware of each one and why. Solution The gravitational force between everyday objects on the surface of the Earth is extremely small. Consider two objects sitting on the floor near each other. They are attracted to each other, but the force of static friction for each is much greater than the gravitational force each experiences from the other. Even in an absolutely frictionless environment, the acceleration resulting from the gravitational force would be so small that it would not be noticeable in a short time frame. We are aware of the gravitational force between objects if at least one of them is very massive, as in the case of the Earth and satellites or the Earth and you. The electric force between two objects is typically zero or close to zero because ordinary objects are typically neutral or close to neutral. We are aware of electric forces between objects when the objects are charged. An example is the electrostatic force (static cling) between pieces of clothing when you pull the clothes out of the dryer.

3 Chapter 21 Question 18 Consider the electric field at the three points indicated by the letters A, B, and C in Fig First draw an arrow at each point indicating the direction of the net force that a positive test charge would experience if placed at that point, then list the letters in order of decreasing field strength (strongest first). Solution At point C, the positive test charge would experience zero net force. At points A and B, the direction of the force on the positive test charge would be the same as the direction of the field. This direction is indicated by the arrows on the field lines. The strongest field is at point A, followed (in order of decreasing field strength) by B and then C.

4 Chapter 21 Problem 3 (I) What is the magnitude of the force a +25μC charge exerts on a +2.5mC charge 28 cm away? Chapter 21 Problem 8 A person scuffing her feet on a wool rug on a dry day accumulates a net charge of -46μC. How many excess electrons does she get, and by how much does her mass increase? Chapter 21 Problem 9 (II) What is the total charge of all the electrons in a 15-kg bar of gold? What is the net charge of the bar? (Gold has 79 electrons per atom and an atomic mass of 197 u.) Chapter 21 Problem 11 (II) Two positive point charges are a fixed distance apart. The sum of their charges is Q T? What charge must each have in order to (a) maximize the electric force between them, and (b) minimize it? Chapter 21 Problem 20 (III) Two small charged spheres hang from cords of equal length, as shown in Fig and make small angles θ 1 and θ 2 with the vertical. (a) If Q 1 =Q, Q 2 =2Q and m 1 = m 2 =m determine the ratio θ 1 /θ 2. (b) If Q 1 =Q, Q 2 =2Q, m 1 =m, and m 2 =2m determine the ratio θ 1 /θ 2. (c) Estimate the distance between the spheres for each case. Chapter 21 Problem 26 (I) What is the electric field at a point when the force on a 1.25μC charge placed at that point is F = (3.0i 3.9j) x 10-3 N?

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