In a 1911, Ernest Rutherford modeled an atom as being a point of positive charge Ze surrounded by a negative charge Ze uniformly distributed in a sphere of radius R centered on the point At distance r within the sphere, the electric fleld is E Ze 40 (1 r2 r(R3) He also gave the electric potential as V Ze 40 (1 r 3 2R r2(2R3) (a) Show how the expression for the electric fleld follows from the expression for V (b) Why does this expression for V not go to zero as r

Question: In a 1911, Ernest Rutherford modeled an atom as being a point of positive charge Ze surrounded by a negative charge - Ze uniformly distributed

In a 1911, Ernest Rutherford modeled an atom as being a point of positive charge Ze surrounded by a negative charge - Ze uniformly distributed in a sphere of radius R centered on the point. At distance r within the sphere, the electric fleld is E = Ze/4πε0 (1/r2 – r(R3). He also gave the electric potential as V = Ze/4πε0 (1/r – 3/2R + r2(2R3) .

(a) Show how the expression for the electric fleld follows from the expression for V.

(b) Why does this expression for V not go to zero as r → ∞?

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