Question

Question3 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 Φ 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 Ds = 5.5 × 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? 0 -Ф (a) Number (b) Number (c) Number Units Units Units

Answer 1

a)

Here

$\phi =5.5\times 10^{5}\times \frac{2}{5}=2.2\times 10^{5}N-m^{2}/C$

The charge of the central particle is

$q_{central}=\varepsilon _{o}\phi =8.8542\times 10^{-12}\times 2.2\times 10^{5}=1.948\times 10^{-6}C(-or-)1.948\mu C$

b)

Here

$\phi =-5.5\times 10^{5}\times \frac{4}{5}=-4.4\times 10^{5}N-m^{2}/C$

Now

$q_{enc}=(-4.4\times 10^{5})(8.8542\times 10^{-12})=-3.895848\times 10^{-6 }C$

$q_{A}=q_{enc}-q_{central}=-3.895848\times 10^{-6 }-1.948\times 10^{-6}=-5.844\times 10^{-6}C (-or-)5.844\mu C$

c)

Here

$\phi=5.5\times 10^{5}\times \frac{6}{5}=6.6\times 10^{5}N-m^{2}/C$

$q_{enc}=6.6\times 10^{5}\times 8.8542\times 10^{-12}=5.844\times 10^{-6}C$

$q_{B}=q_{enc}-q_{A}-q_{central}=5.844\times 10^{-6}-(-5.844\times 10^{-6})-1.948\times 10^{-6}$

$q_{B}=9.74\times 10^{-6}C (-or-)9.74\mu C$