A charged conducting sphere is at the center of a charged, hollow metal sphere.

Question

A charged conducting sphere is at the center of a charged, hollow metal sphere. The central sphere has a charge of +Q and the shell has a uniformly distributed charge of -Q. (a) Select the appropiate shape of the Gaussian surface that we could use to enclose the spherical conductors in this problem such that the electric field across the Gaussian surface is constant. Cone Sphere Pyramid Square Box Cylinder Rectangular Box (b) What is the surface area of a spherical Gaussian surface with a radius of r? (Use pi for ) Click here to preview your answer. (c) Assume that the magnitude of the electric field at the Gaussian spherical surface from part (a) is given by E. For the Gaussian surface centered on the conducting spheres in the above figure, what is the electric flux in terms of E and r? (Use pi for ) Click here to preview your answer. (d) What is the electric flux equal to in terms of the charge enclosed by the Gaussian surface (q_in) and the constant 0 (use e_0 for 0)? Click here to preview your answer. (e) Your answers to parts (c) and (d) are both equal to the electric flux, so equate them and solve for the magnitude of the electric field at our Gaussian surface in terms of its radius (r) and the charge enclosed by the surface (q_in). (Use pi for , and use e_0 for 0) Click here to preview your answer. Hopefully, your answer looks VERY familiar! (f) What is the magnitude of the electric field inside the central conductor, where r < a, where k = 1/(40). HINT: What is the total charge is enclosed by the Gaussian surface? -kQ/r2 0 -kQ2/r2 kQ/r2 kQ2/r2 (g) What is the magnitude of the electric field in the space between the central conductor and the shell where a < r < b, where k = 1/(40). -kQ2/r2 kQ2/r2 kQ/r2 0 -kQ/r2 (h) What is the magnitude of the electric field in the region outside the shell, where r > c, where k = 1/(40). -kQ2/r2 kQ/r2 -kQ/r2 0 kQ2/r2

Explanation / Answer

a) sphere

b) 4*pi*r^2

c) E*4*pi*r^2

d) E*4*pi*r^2 = q_in/epsilon

e) E =(1/4*pi*epsilon)*q_in/r^2

f) k*Q/r^2

g) 0

h) 0

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