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Physics Midterm 2 Exam for University Student - Fall 2004, Exams of Engineering Physics

The fall 2004 physics 7b midterm 2 exam for university students. The exam covers various topics in physics, including electrostatics, electric fields, capacitance, and projectile motion. Students are required to solve problems related to these topics and express their answers in terms of given quantities.

Typology: Exams

2012/2013

Uploaded on 02/12/2013

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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.
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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 C 1 is charged to a potential difference V 0. The charging battery is then removed and the capacitor is connected as in the figure to an uncharged capacitor C 2. (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 V 0. 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.

  1. 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.
  1. (a) A particle of mass m and charge q is placed at rest in the uniform electric field of a cathode-ray oscilloscope (see figure) and released. Write an equation for its position (x, y) as a function of time. (b) Suppose the electric field between the plates is 1.2x10 4 N/C. What deflection (y) will an electron experience if it enters at right angles to the field with a kinetic energy of 2000 eV (=3.2x10-16^ J), a typical value? The deflecting assembly is 1.5 cm long.
  2. The figure below shows six concentric conducting spheres, A, B, C, D, E, and F, having radii R, 2R, 3R, 4R, 5R, and 6R, respectively. Spheres B and C are connected by a conducting wire as are spheres D and E. Determine the equivalent capacitance of this system.