A charged particle is held at the center of two concentric conducting spherical

Question

A charged particle is held at the center of two concentric conducting spherical shells. 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 s 9.0x 105 N-m2/c. 0 -, (a) What is the charge of the central particle? 1.593E-6 X If you mentally construct a Gaussian sphere concentric with the smaller shell but with a smaller radius, what do the plotted flux and Gauss' law reveal about the charge enclosed by the sphere, hence that of the particle? How about a Gaussian sphere with a radius between the radii of the two shells? uC (b) What is the net charge of shell A? HC (c) What is the net charge of shell B: HC

Explanation / Answer

a)

Net flux, p= 9*9*10^5/5= 16.2 *10^5

Using gauss theorem

q= p* epsiolon_not

= 16.2*10^5*8.85*10^-12

= - 14.33 uC

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b)

Now ,

p'= 4/5*9*10^5= 7.2*10^5

q'= 7.2*10^5*8.85*10^-12= 6.372*10^-6 C

Charge on shell A

qA= 6.372*10^-6 - (- 14.33)*10^-6

= 20.7 uC

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c).

p''= (2/5)*9*10^5= 3.6*10^5

q= 3.6*10^5*8.85*10^-12

q= - 3.186*10^-6 C

Charge on shell B

qb= - 3.186*10^-6 - 20.7*10^-6 - (- 14.33)*10^-6

qb= -9.556 uC

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Good luck

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