PHYSICS 7b MIDTERM 2
Prof. C. F. McKee Nov 2, 2009
Partial credit will be given, so show your reasoning carefully. The number of points for each
problem is listed at the left. You are permitted one 3x5 card of notes, written on both sides.
Relevant constants are given at the end.
1. [10] A D battery that costs $1.70 delivers 25 mA at 1.5 V for 820 hr. What is the ratio of the
cost of this power to that from the 120 V power we get from the wall socket, at $0.10 per kwh?
2. [15] (Giancoli 23-15.) Consider two conducting spheres, of radius r1and r2. The spheres are
separated by a distance much greater than the size of either one. Initially, the first sphere has
a charge Qand the second one is uncharged. The two are then connected by a conducting wire.
What is the charge on the second sphere once a steady state is reached?
3. [15] An electron is fired through a tiny hole into a capacitor at a velocity of 107m s−1. The
capacitor is charged so that the field inside is E= 2.6×104V m−1, pointing in the direction of the
electron velocity. The capacitor plates are separated by a distance dsuch that the electron comes
to rest just as it reaches the second plate. Find d.
4. [15] Two infinite insulating slabs of thickness dare placed one on top of the other. The top slab
has a uniform volume charge density ρand the bottom one has a uniform volume charge density
−ρ. There are no other charges. Find E(z) for all z, where ˆzis normal to the surfaces of the slabs
and z= 0 on the plane between the slabs.
5. [20] Two capacitors, C1and C2, with C2> C1are connected in series with a battery of potential
V0, and the energy in the capacitors is measured to be U. If instead, the capacitors are connected
in parallel to the same battery, the total energy is found to be 5U.
a) [10] For the case of the capacitors in series, show that the sum of the energies in the two
capacitors is the same as the energy of the equivalent single capacitor. (The same is true for
the parallel capacitors, but you need not show that.)
b) [10] What is the ratio C2/C1?
