Fall ‘12 PHY 122 Homework Solutions #2

Chapter 21 Problem 40 Two parallel circular rings of radius R have their centers on the x

axis separated by a distance l , as shown in Fig. 21–60. If each ring carries a uniformly distributed charge Q, find the electric field, at E(x) points along the x axis.

Chapter 21 Problem 41

(a) Two equal charges Q are positioned at points (x=l, y=0) and (x=-l,

y=0). Determine the electric field as a function of y for points along

the y axis. (b) Show that the field is a maximum at .

Chapter 21 Problem 61 A positive charge q is placed at the center of a circular ring of radius R. The ring carries a uniformly distributed negative charge of total magnitude 2Q. (a) If the charge q is displaced from the center a small distance x as shown in Fig. 21–69, show that it will undergo simple harmonic motion when released. (b) If its mass is m, what is its period?

Chapter 22 Question 4 What can you say about the flux through a closed surface that encloses an electric dipole? Solution The net flux will be zero. An electric dipole consists of two charges that are equal in magnitude but opposite in sign, so the net charge of an electric dipole is zero. If the closed surface encloses a zero net charge, than the net flux through it will be zero. Chapter 22 Question 11 A point charge Q is surrounded by a spherical surface of radius r0, whose center is at C. Later, the charge is moved to the right a distance ½ r0, but the sphere remains where it was, Fig. 22–23. How is the electric flux FE through the sphere changed? Is the electric field at the surface of the sphere changed? For each “yes” answer, describe the change.

Solution The electric flux through the sphere remains the same, since the same charge is enclosed. The electric field at the surface of the sphere is changed, because different parts of the sphere are now at different distances from the charge. The electric field will not have the same magnitude for all parts of the sphere, and the direction of the electric field will not be parallel to the outward normal for all points on the surface of the sphere. The electric field will be stronger on the side closer to the charge and weaker on the side further from the charge.

Chapter 22 Problem 2 The Earth possesses an electric field of (average) magnitude 150 N/C near its surface. The field points radially inward. Calculate the net electric flux outward through a spherical surface surrounding, and just beyond, the Earth’s surface. Chapter 22 Problem 3 A cube of side l is placed in a uniform field E0 with edges parallel to the field lines. (a) What is the net flux through the cube? (b) What is the flux through each of its six faces? Chapter 22 Problem 6 Figure 22–26 shows five closed surfaces that surround various charges in a plane, as indicated. Determine the electric flux through each surface S1,S2,S3,S4 and S5. The surfaces are flat “pillbox” surfaces that extend only slightly above and below the plane in which the charges lie.

Chapter 22 Problem 9 In a certain region of space, the electric field is constant in direction (say horizontal, in the x direction), but its magnitude decreases from E = 560 N/C at x = 0m to E = 410N/C at x = 25m. Determine the charge within a cubical box of side l = 25m, where the box is oriented so that four of its sides are parallel to the field lines (Fig. 22–28).

Chapter 22 Problem 21 A spherical cavity of radius 4.50 cm is at the center of a metal sphere of radius 18.0 cm. A point charge Q = 5.50μC rests at the very center of the cavity, whereas the metal conductor carries no net charge. Determine the electric field at a point (a) 3.00 cm from the center of the cavity, (b) 6.00 cm from the center of the cavity, (c) 30.0 cm from the center.

Chapter 22 Problem 34 A very long solid nonconducting cylinder of radius R0 and length l (R0 << l) possesses a uniform volume charge density ρE C/m3. Fig. 22–34. Determine the electric field at points (a) outside the cylinder (R > R0) and (b) inside the cylinder (R < R0). Do only for points far from the ends and for which R << l.