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 o 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 Os = 4.5 x 105 N·m2/C. What are (a) the charge of the central particle and the net charges of (b) shell A and (c) shell B? B А (10 N·mº/C) 0 -20, ( a )

Answer 1

The flux of the particle is given by , = -1.80,= -8.10% 10%Nm2/C. As €0 = Lenc then qp = 8.85 x 10-12.-8.1x 105 = - 7.17 MC

Outside of shell A, the flux takes the value A That gives us the total charge enclosed inside A: 89, =3.60x 105Nm2/C. Genc = 8.85 x 10-12.3.6 x 105 = + 3.2 uc As Genc = 9A + 9p and we already know qp, then 4A = Lenc - 9p = + 10.4 C

Finally, the flux outside of shell B is 08 = -.40, = -1.80 x 105Nm2/C. By the same process: Genc = 8.85 x 10-12.-1.8 x 10 = -1.6 UC As before, we can deduct the charges we've already found: 98 = lenc - 9A - 9p = -1.64C

(a) -7.17μC (b) +10.4 μC (c) -1.64μC

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