1. (25 pts)
a) (5 pts) Two charged, insulating spheres are slightly intermeshed such that they overlap a bit. How
would you go about computing the electric field in the region of overlap?
It is easy to work out the electric field somewhere inside a single sphere with Gauss’s Law. So compute
the field from each sphere individually. Then use the principle of superposition to add these two
contributions to obtain the net field.
b) (5 pts) The electric field near a large sheet of charge with a positive surface charge density σis
~
E=σ/2ǫ0away from the sheet. What would be the electric field in the region between two large
parallel sheets of charge if one had positive charge density σand the other a negative charge density
−σ?
+σ −σ
The field from the negatively charged sheet will point towards it. Thus both field contributions will be
in the same direction. Summing these two contributions gives
E=σ
ǫ0
c) (5 pts) A charged particle is in a uniform electric field. Explain why the equations of kinematics may
be used to predict the motion of this particle.
Since both the charge and electric field are constant, the force exerted on the charge is constant. As
long as the mass of the charge is constant, its acceleration is also constant. The equations of kinematics
were developed from an assumption of constant acceleration, thus can be used in this case.
d) (5 pts) Briefly explain why the electric field immediately outside of a conductor must be perpendic-
ular to the surface of the conductor in the study of electrostatics.
If the electric field were in a direction other than normal to the surface, there would be a force compo-
nent acting on charges in the conductor parallel to the surface causing them to accelerate rather than
reach equilibrium. This is not electrostatics. Thus the field must be perpendicular to the surface for
electrostatic cases.
e) (5 pts) Why is the net electric flux through a closed surface which contains no net charge zero? Do
not use any mathematics in your explanation.
If there is no source (or sink) of new field lines within the surface, all field lines originating outside of
the surface must both enter and exit the surface yielding a net flux of zero.
