Download cp9

Lesson 9
(1) A parallel plate capacitor is made up of a pair of
circular metal plates of radius 25cm separated by a
distance of 1.0cm. The plates are connected to the
terminals of a voltage source that delivers 160V. Find
(a) the capacitance
(b) the stored charge,
(c) the stored energy,
(d) the electric field between the plates.
(2) What is the highest voltage that can be safely
carried by the capacitor of the previous problem if
the breakdown electric field of air is 3 MV/m?
(3) After charging a parallel plate capacitor and
disconnecting the voltage source, the distance
between the plates is reduced.
1. Does the voltage increase or decrease?
2. Does the energy stored increase or decrease?
3. Is mechanical work required to move the
plates?
(4) Repeat problem (3) if the distance is reduced
while the plates are still connected to the voltage
source.
(5) After charging, the plates of the capacitor of
Problem 1 are disconnected from the voltage source.
The separation of the plates is now reduced to 0.7cm.
Find the new energy stored.
(6) Find the electrostatic energy of a thin spherical
shell of radius R carrying a total charge Q.
(7) A co-axial cable consists of an inner cylindrical
shell of radius a and an outer shell of radius b, both
of length L. The inner shell carries a line charge
density λ. Use Gauss law to determine the electric
field at a point a distance r from the axis where
a<r<b, assuming L can be considered infinite. By
integration, find the potential difference between the
shells. Hence find an expression for the capacitance
of the cable.