A large metal sphere has three times the diameter of a smaller sphere and carrie

Question

A large metal sphere has three times the diameter of a smaller sphere and carries three times as much charge. Both spheres are isolated, so their surface charge densities are uniform.

PART A

Compare the potentials at their surfaces for the larger sphere's surface potential

Larger sphere's field surface strength:

A) 3 times greater than that of the smaller sphere B) 3 times less than that of the smaller sphere C) 9 times greater than that of the smaller sphere D) 9 times less than that of the smaller sphere E) equals to that of the smaller sphere

Explanation / Answer

(a) The potential of an isolated metal sphere, with charge Q and radius R, is kQ=R, so a sphere with charge 3Q and radius 3R has the same potential

E) equals to that of the smaller sphere

b)  However, the electric field at the surface of the smaller sphere is ?=? 0 = kQ=R2 , so tripling Q and R reduces the surface field by a factor of 1/3

B) 3 times less than that of the smaller sphere

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