Flux and nonconducting shells. A charged particle is suspended at the center of
ID: 1590409 • Letter: F
Question
Flux and nonconducting shells. A charged particle is suspended at the center of two concentric spherical shells that are very thin and made of nonconducting material. Figure 23-37u shows a cross section. Figure 23-376 gives the net flux psi through a Gaussian sphere centered on the particle, as a function of the radius r of the sphere. The scale of the vertical axis is set by psi_s = 5.0 X 10^5 N m^2/C. (a) What is the charge of the central particle? What are the net charges of (b) shell A and (c) shell B?Explanation / Answer
Charge enclosed = o
o = 8.85 x 10-12 F/m
a)
Flux at r<rA is entirely due to the charge inside.
q = 2 x 105 x 8.85 x 10-12 = 1.77 x 10-6 C
b)
Total flux = -5 x 105
Take the charge on the shell A as qA
q + qA = -5 x 105 x 8.85 x 10-12 = -4.425 x 10-6 C
qA = -4.425 x 10-6 C - 1.77 x 10-6 C = -6.195 x 10-6 C
c)
Total flux = 6 x 105
Charge on the shell B be qB
q + qA + qB = 6 x 105 x 8.85 x 10-12 = 5.31 x 10-6 C
qB = 5.31 x 10-6 C - (q + qA)
= 5.31 x 10-6 C - (-4.425 x 10-6) = 9.735 x 10-6 C