Flux and nonconducting shells. A charged particle is suspended at the center of
ID: 3308240 • 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 (a) shows a cross section. Figure b) gives the net flux 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 d s-3.0 x 105 N-m2 c. (a) What is the charge of the central particle? What are the net charges of (b) shell A and (c) shell B? (a) Number (b) Number (c) Number Units Units UnitsExplanation / Answer
The vertical axis is marked as
s= 3.0*105 Nm2/C
(a)
From fig we have,
s = 105 Nm2/C (in SI units)
qcentral = (8.85*10-12 C2/Nm2)(105Nm2/C)
= +8.85 * 10-7 C
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(b)
The next value that s = – 20.0 × 105 Nm2/C
which implies,
qenc = (8.85*10^-12 C2/Nm2)(-20 ×10^5)
= -177* 10-7 C
The charge onshell A is,
qA = qenc –qcentral
= -177* 10-7 C - 8.85* 10-7 C
= -168.15 * 10-7 C
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(c)
Finally, s =30.0× 105 Nm2/C
whichimplies total enclosed charge
q total enclosed = (8.85*10-12 C2/Nm2)(30 ×10^5)
= 26.55*10-6C
= 26.55µC
then the charge on B is
qtotal enc.- qA - qcentral
= 26.55µC-(-26.55µC)-0.85µC
= 25.25 µC