Question

Three metal spheres (A, B, C) all have the same charge +Q on them. The spheres have radii of R_A = 1m, R_B = 2m, and R_C = 4m respectively. Rank the magnitude of the electric field at a distance r = 3m in each case.

a. E_A < E_B < E_C

b. E_C < (E_A = E_B)

c. E_A = E_B = E_C

d. E_C < E_B < E_A

Answer 1

Using Gauss law,
E_A * 4r² = Q_enc / o
Where EA is the electric field of sphere A, r is the radius of the Gaussian surface, Q_enc is the charge enclosed in the Gaussian sphere.
Q_enc = Q since r > R_A
E_A = Q / 4or²

Similarly for sphere B,
E_B * 4r² = Q_enc / o
Where E_B is the electric field of the sphere, Q_enc is the charge enclosed in the Gaussian sphere.
Q_enc = Q since r > R_B
E_B = Q / 4or²

For sphere C,
E_C * 4r² = Q_enc / o
Where E_C is the electric field of the sphere, Q_enc is the charge enclosed in the Gaussian sphere.
Q_enc = 0 since r < R_C, for metal spheres, all the charge will remain on the surface
E_C = 0

So, EC < (EA = EB) (option B)