7. Since the charge is uniformly distributed throughout a sphere, the electric field at the surface is exactly
the same as it would be if the charge were all at the center. That is, the magnitude of the field is
E=q
4πε0R2
where qis the magnitude of the total charge and Ris the sphere radius. The magnitude of the total
charge is Ze,so
E=Ze
4πε0R2=(8.99 ×109N·m2/C2)(94)(1.60 ×10−19 C)
(6.64 ×10−15 m)2=3.07 ×1021 N/C.
The field is normal to the surface and since the charge is positive, it points outward from the surface.
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