1) Consider Fig, which shows three pith balls and their corresponding net charges. Several notional surfaces have been drawn that enclose some or all of the charges. (A 2-D outline of each surface is shown). Use Gauss' Law to determine the electric flux through each of the surfaces.
2) A +4μC point charge is placed in the center of a hemisphere of radius one meter as shown.
a) Use Gauss' Law to find the electric flux through the hemisphere.
b) The point charge is moved one meter to the left. Which of the following best describes the electric flux through the hemisphere with the charge at this position? Explain your choice.
i. The electric flux is zero.
ii. The electric flux is the same as in part a (but not zero).
iii. The electric flux is larger than in part a.
iv. The electric flux is smaller than in part a.
3) Consider a spherical insulator with net charge Q that has a uniform charge distribution within it (p = Q/V) throughout its volume.
a) Use Gauss' Law to show that the electric field inside the surface of the sphere is given by:
E = ρ/3∈0 r
b) Show that the electric field outside the surface of the sphere is equivalent to the electric field of a point charge of magnitude Q at the center of the sphere.