Continued on back
Physics 7b
Fall 2004
Midterm 2
Ramesh
All algebraic answers should be expressed in terms of the given quantities. Box your final
answer and show all your work. All problems are worth the same number of points.
1. A particle of mass m, charge q>0 and initial kinetic energy K is projected (from
“infinity”) towards a heavy nucleus of charge Q, assumed to have a fixed position in our
reference frame.
(a) If the “aim is perfect,” how close to the center of the nucleus is the particle
when it comes to rest?
(b) With a particular imperfect aim the particle’s closest approach to the nucleus
is twice the distance determined in part a. Determine the speed of the particle at this
closest distance of approach.
2. A capacitor C1 is charged to a potential difference
V0. The charging battery is then removed and the
capacitor is connected as in the figure to an uncharged
capacitor C2.
(a) What is the final potential difference V
across the combination?
(b) What is the stored energy before and after the switch S is thrown?
(c) (independent of parts a and b) A parallel plate capacitor has plates with area A
and separation d. A battery charges the plates to a potential difference V0. The battery is
then disconnected and a dielectric slab of area A, thickness d and dielectric constant
is
introduced. Calculate the stored energy both before and after the slab is introduced.
Explain how total energy is conserved in this case.
3. A sphere of radius 2a is made of a non-conducting
material that has uniform volume charge density . A
spherical cavity of radius a is now removed from the
sphere as shown in the figure. Find the electric field
(magnitude and direction) at the point x=-a/2, y=a.
