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A nonconducting sphere with center C and radius a has a spherically symmetric electric charge density. The total charge of the object is Q > 0.

a. Determine the magnitude and direction of the electric field at point P, which is a distance R > a to the right of the sphere's center.

b. Determine the flux of the electric field through the spherical surface centered at C and passing through P.

A point particle of charge Q is now placed a distance R below point P. as shown above.

c. Determine the magnitude and direction of the electric field at point P.

d. Now consider four point charges, q1, q2, q3, and q4, that lie in the plane of the page as shown in the diagram above. Imagine a three dimensional closed surface whose cross section in the plane of the page is indicated.

i. Which of these charges contribute to the net electric flux through the surface?

ii. Which of these charges contribute to the electric field at point P1 ?

iii. Are your answers to i and ii the same or are they different? Explain why this is so.

e. If the net charge enclosed by a surface is zero, does this mean that the field is zero at all points on the surface? Justify your answer.

f. If the field is zero at all points on a surface, does this mean there is no net charge enclosed by the surface? Justify your answer.