In: Physics
1. An infinitely long non-conducting right-circular cylinder of
radius a, oriented concentrically with the z-axis, carries uniform
charge density ?0. It is surrounded concentrically by an infinite
long grounded right-circular conducting cylindrical shell of inner
radius b and outer radius c. Ground potential is zero.
(a) (4 points) What is the linear charge density (charge per unit
length) ? of the inner nonconducting cylinder.
(b) (4 points) What are the linear charge densities (charge per
unit length) ? on the surfaces of the conducting shell at ?=? and
?=?, where ? is the radial cylindrical coordinate measured from the
z-axis?
(c) (12 points) What is the electric field in the regions
?<?,?<?<?,?<?<?, and ?>??
2. (20 points) For the configuration in Problem 1, what is the electric potential along the z-axis, i.e. at ?=0, assuming the ground potential is zero?
3. An ideal parallel plate capacitor with capacitance ?0 is
charged to potential ∆?0. How much work is done in terms of ?0 and
∆?0 (the initial potential difference between the plates) in
separating the plates to double their initial separation
when:
(a) (10 points) the plates are charged to potential difference ∆?0
and insulated, i.e. removed from the charging battery, before being
separated;
(b) (10 points) the plates are permanently connected to a battery
which maintains a potential difference ∆?0 between the plates while
they are being separated?
(Your answers to this problem must be expressed in terms of ?0 and
∆?0, not in terms of the charge on the plates, since that is not a
given quantity.)
Questions involving charge densities,electric fields and electric potentials at different locations of a system consisting of charged dielectric and grounded conductor having cylindrical symmetry