3-10. The electric field from a charged sphere of 10 cm radius is 20 kV mat a distance of 20 cm from the center of the sphere. Assuming uniform charge distribution on the surface of the sphere, find: (a) the D field; (b) the total charge on the sphere.

A thin nonconducting rod with a uniform distribution of positive charge Q is bent into a circle of radius R (Fig.22-48). The central perpendicular axis through the ring is a z axis, with the origin at the center of the ring. Whatis the magnitude of the electric field due to the rod at (a) z = 0 and (b) z = ∞? (c) In terms of R, at what positivevalue of z is that magnitude maximum? (d) If R = 2.00 cm and Q = 4.00 μC, what is the maximum magnitude?

The electric field everywhere on the surface of a charged sphere of radius 0.204 m has a magnitude of 510 N/C and points radially outward from th center of the sphere. (a) What is the net charge on the sphere? ]nc (b) What can you conclude about the nature and distribution of charge inside the sphere? Thie anewer hae not hean graded vet

+20 +0 +20 Four point charges of varying magnitude and sign are arranged on the corners of the square of side d as shown in Fig. 21-6. Which of the arrows shown represents the net electric field acting on the point charge with a charge +Q? O D O A O none of the given choices O C O B

47. (III) A flat slab of nonconducting material has thickness 2d, which is small compared to its height and breadth. Define the x axis to be along the direction of the slab's thickness with the origin at the center of the slab (Fig. 22-41). If the slab carries a volume charge density PE(x) the region -d < x <0 and PE(x) = +po in the region 0 < xs +d, determine the electric field E as a function of x in the regions (a) outside the slab, = -Po in (b) 0 < x < +d, and (c) -d s x < 0. Let po be a positive constant. - +d FIGURE 22-41

38 In Fig. 23-48a, an electron is shot directly away from a uni- formly charged plastic sheet, at speed v, = 2.0 x 10° m/s. The sheet is nonconducting, flat, and very large. Figure 23-48b gives the electron's vertical velocity component v versus time t until the return to the launch point. What is the sheet's surface charge density? 12 -e t (ps) (a) (b) v (10 m/s)

Figure 22-40 shows an electric dipole. What are the (a) magni- tude and (b) direction (rèlative to the positive direction of the x axis) of the dipole's electric field at point P, located at distance r> d? +q d/2 d/2 Fig. 22-40 Problem 19.

3 In Fig. 22-24, two particles +3q of charge -q are arranged symmetrically about the y axis; each produces an elec- tric field at point P on that axis. (a) Are the magnitudes of the fields at P equal? (b) Is each electric field directed toward or away from the charge producing it? (c) Is the magnitude of the net electric field at P equal to the sum of the magnitudes E of the two field vec- tors (is it equal to 2E)? (d) Do the x components of those two field vec- tors add or cancel? (e) Do their y components add or cancel? (f) Is +6q -29 Figure 22-23 Question 2. -4 -4 the direction of the net field at P that of the canceling components or the adding components? (g) What is the direction of the net field? Figure 22-24 Question 3. TO

•34 In Fig. 23-45, a small circular hole of radius R = 1.80 cm has been cut in the middle of an infinite, flat, nonconducting surface that has uniform charge density o = 4.50 pC/m?. A z axis, with its origin at the hole's center, is perpendicular to the surface. In unit- vector notation, what is the electric field at point Pat z = 2.56 cm? (Hint: See Eq. 22-26 and use superposition.) Figure 23-45 Problem 34.