Problem 1:
A two electron system has (in its center of mass frame) energy E and angular momentum L. What is the closest distance the electrons approach each other?
Problem 2:
Two isolated spherical conductors of radii 3 cm and 9 cm
are charged to 1500 V and 3000 V, respectively. They are very far away from
each other.
(a) What is the total energy of the system?
(b) If we connect the two conductors by a fine wire and
wait until equilibrium is established, how much heat will be generated in the
wire?
Problem 3:
A conducting sphere of radius a carrying a charge q is submerged halfway into a non-conducting dielectric liquid of dielectric constant e. The other half is in air. Will the electric field be purely radial? Explain.
Problem 4:
The dielectric of a parallel plate capacitor has a permittivity that varies as e1 + ax, where x is the distance from one plate. The area of a plate is A and their spacing is s.Problem 5:
(a) A spherical dielectric of radius a has a uniform polarization
P in the z-direction. Show that the electric field inside the
dielectric due to the polarization is given by E = -P/(3e0).
(b) A large capacitor in vacuum has parallel circular plates of radius R
separated by a distance d (d<<R). The capacitor is charged to a
potential difference V and disconnected from the source. Find the energy
stored in the capacitor.
(c) Subsequently, a small sphere of radius a (a<<d) and
dielectric constant K is placed in the center of the capacitor between
the plates. Find the electric field inside the dielectric.
(d) Will the capacitor have less, more, or the same energy than before the
dielectric was inserted? Explain!
Problem 6:
A parallel-plate capacitor is connected to a battery which maintains a
potential difference V0 between its plates. A slab of
dielectric constant K is inserted between the plates, completely filling the
space between them.
(a) Show that the battery does an amount of work q0V0(K -
1) during the insertion process, if q0 is the charge on the capacitor
plates before the slab is inserted.
(b) How much work is done by mechanical forces on the slab when it is inserted
between the plates? Is this work done on, or by, the agent inserting the
slab?
Problem 7:
Regarding the Earth and a cloud layer 800 m above the Earth as the plates of a capacitor, calculate the capacitance if the cloud layer has an area of 1 km2. If an electric field of 3x106 N/C makes the air break down and conduct electricity, (that is, cause lightning,) what is the maximum charge (in C) the cloud can hold?