47. When the drop is in equilibrium, the force of gravity is balanced by the force of the electric field: mg = qE, where m is the mass of the drop, q is the charge on the drop, and E is the magnitude of the electric field. The mass of the drop is given by
19. (a) The charge on the surface of the sphere is the product of the surface charge density and the surface area of the sphere (which is 4r 2 , where r is the radius). Thus,
1.2 m 6 5 2 q = 4r = 4 ( 8.1 10 C/m ) = 3.7 10 C. 2
2 2
(b) We choose a Gaussia
18. Eq. 23-6 (Gauss law) gives = qenc. (a) The value = 9.0 105 N m 2 /C for small r leads to qcentral = 7.97 106 C or roughly 8.0 C. (b) The next (non-zero) value that takes is = +4.0 105 N m 2 /C , which implies qenc = 3.54 106 C. But we have already acc
17. (a) The area of a sphere may be written 4R2= D2. Thus, q 2.4 106 C = = = 4.5 107 C/m 2 . 2 2 D (1.3 m ) (b) Eq. 23-11 gives E=
4.5 107 C/m 2 = = 5.1 104 N/C. 2 2 12 0 8.85 10 C / N m