Ex. 1) A metal sphere with radius ra is supported on an insulating stand at the

Question

Ex. 1) A metal sphere with radius ra is supported on an insulating stand at the center of a hollow, metal, spherical shell with radius rb. There is charge +q on the inner sphere and charge -q on the a) Calculate the potential V(r) for ter calcula Ta outer spherical shell. i) rTa ili) r>r (Hint:The net potential is the sum of the potentials due to the individual Show that the potential of the inner sphere with respect to the outer is spheres.) Take V to be zero when r is infinite. b) o) Show that the elecric feld at any point be peres as magaitude c) Show that the electric field at any point between the spheres has magnitude Vab Find the electric field at a point outside the larger sphere at a distance r from the center, where r > Tb Suppose the charge on the outer sphere is not -q but a negative charge of different magnitude, say-Q. d) e)

Explanation / Answer

a) i) V ( for r < ra) = kq/ ra + k(-q)/rb= kq ( 1/ra - 1/rb)

a) ii) V ( ra < r < rb) = kq/ r + k(-q)/rb = kq ( 1/r - 1/rb)

a) iii) ( r > rb) = kq/ r - kq/ r = 0 V

d) This is a spherically symmetric charge distrbution with a net charge 0, therefore, E ( r > rb) = 0

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