In the figure a sphere, of radius a = 15.0 cm and charge q = 7.00×10 -6 C unifor

Question

In the figure a sphere, of radius a = 15.0 cm and charge q = 7.00×10-6 C uniformly distributed throughout its volume, is concentric with a spherical conducting shell of inner radius b = 30.0 cm and outer radius c = 32.0 cm . This shell has a net charge of -q.

1.) Find expressions for the electric field, as a function of the radius r, within the sphere and the shell (r < a). Evaluate for r = 7.5 cm.

2.) 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=22.5 cm.

3.) Find expressions for the electric field, as a function of the radius r, inside the shell (b < r < c). Evaluate for r = 31.0 cm.

4.) Find expressions for the electric field, as a function of the radius r, outside the shell (r > c). Evaluate for r = 33.0 cm.

5.) What is the charge on the outer surface of the shell?

Explanation / Answer

1) Case I: Inside the inner sphere Since it is inside a conductor, E = 0

2) Between the inner and the outer sphere

E(4*pi*r^2) = 4*pi*k(-Q)

so, E = -k *Q / r^2

3)  Inside the outside spherical shell Since it is inside a conductor, we get E= 0

4) Outside the outer spherical shell The charge enclosed by any gaussian surface would be 2*7*10^-6 + (Q ) = Q . Thus, the electric field would be

E = k*Q / r^2

Plug in the values

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