In the figure a sphere, of radius a = 11.4 cm and charge q = 1.00×10-5 C uniform

Question

In the figure a sphere, of radius a = 11.4 cm and charge q = 1.00×10-5 C uniformly distributed throughout its volume, is concentric with a spherical conducting shell of inner radius b = 39.9 cm and outer radius c = 41.9 cm . This shell has a net charge of -q. 24-34.jpg (Figure Included Here)

Find expressions for the electric field, as a function of the radius r, within the sphere and the shell (r < a). Evaluate for r = 5.7 cm.

Find expressions for the electric field, as a function of the radius r, between the sphere and the shell (a < r < b). Evaluate for r=25.6 cm.

Find expressions for the electric field, as a function of the radius r, inside the shell (b < r < c). Evaluate for r = 40.9 cm.

Find expressions for the electric field, as a function of the radius r, outside the shell (r > c). Evaluate for r = 42.9 cm.

What is the charge on the outer surface of the shell?

Explanation / Answer

Here,

The charge enclosed by the Gaussian surface = q1(r/a)^3
Therefore, Gauss' Law :
4 * *r^2 *E = (q1/0) * (r/a)^3

E = (q1*r)/(4**e0*a^3)


E = [(1 * 10^-5 C) * (5.7 * 10^-2 m)] / [4** (8.85*10^-12 N*m^2/C^2) * (11.4 * 10^-2 m)^3]
E = 3.45E-7 / 2.9227E-13 = 3.46 * 10^6 N/C

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