Flux and nonconducting shells . A charged particle issuspended at the center of

Question

Flux and nonconducting shells. A charged particle issuspended at the center of two concentric spherical shells that arevery thin and made of nonconducting material. Figure (a) belowshows a cross section. Figure (b) below gives the netflux through a Gaussian sphere centered onthe particle, as a function of the radius r ofthe sphere. The scale of the vertical axis is setby s = 6.0 ×105 N·m2/C. (a) Whatis the charge of the central particle? Give your answers inµC. What are the net chargesof (b) shell A and (c) shell B?

Explanation / Answer

Flux is just = Q/ a. Picking off the graph the flux () from thecenter to sphere A is = 2.0 x105 N-m2/C = 8.85 x10-12 C2/N-m2 ergo the charge at the center is Qc = Qc = 1.77x10-6 C = 1.77 µC b. The flux at sphere A to B is -4 x 105N-m2/C therefore the difference across A is -6 x105 N-m2/C. This is just -3xQc, ergo Qa = -3 * Qc Qa= -5.31 C c. Similarly, the difference across sphere B is 10x 105 N-m2/C and Qa= -5.31 C c. Similarly, the difference across sphere B is 10x 105 N-m2/C and Qb= 8.85 C Note: The scale on the graph has s=5x10-5, but your question states s =6x10-5. I solved it for s=5x10-5. Multiply everything by 6/5th if thewritten question is correct.

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