GENERAL PHYS-102: PHYSICS II
Midterm I, Mar. 10, 2007 Duration: 120 minutes
NAME....ID No..
Q1
Q2
Q3
Q4
Q5
Total
Instructions:
1. Read questions carefully. If you do not understand meaning of English words, ask your assistant for explanations. 2. Write solution with clarity and necessary comments (explanations). 3. Use legible writing especially in formulas. 4. Do not forget to check your results by means of analysis of dimensions. Useful integrals: x x 1 2 2 x 2 d 2 dx x d x 2 d 2 3 / 2 dx x 2 d 2 1 1 1 x 2 2 x 2 d 2 dx d arctan( d ) x 2 d 2 dx ln( x x d )
1 1 dx d x 2 d 2 d 2 ln( x x 2 d 2 ) 2 2 x2 d 2 1 x x 2 d 2 3 / 2 dx d 2 x 2 d 2
x2
1 +
Binomial expansion: ( 1) 2 = 1 + + + 2
( 1)
Note: Solutions will be available at physics.bilkent.edu.tr/phys102.html just after the exam.
GOOD LUCK
Question 1: A proton with kinetic energy K = 2106 eV is fired perpendicular to the face of a infinite insulating plate which has a uniform surface charge density = 910-6 C/m2. (See the figure given below.) a) Find the magnitude and the direction of the electric field ( E ) due to the metal plate. b) Find the magnitude and the direction of the force ( F ) on the proton. c) Find the distance d that the proton must be fired so that it stops right at the surface of the plate. (0 910-12 C2/Nm2, e 1.610-19 C, 1eV 1.610-19 J)
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Question 2: Below figure shows an electric quadrupole. It consists of two dipoles with dipole moments that are equal in magnitude but opposite in direction (Both q charges are at z=0). a) Find the electric field ( E ) at point P. b) For z >> d, show that the value of electric field ( E ) on the axis of quadrupole for point a P a distance z from its center is given by
40 z 4 in which Q (= 2qd ) is known as the quadrupole moment of the charge distribution.
2
E=
3Q
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Question 3: In an historic 1911 paper, Ernest Rutherford used the following simple model of atom to get some idea of the forces required to deflect an -particle through a large angle: consider an atom *as+ containing a point positive charge Ze at its center and surrounded by a distribution of negative electricity Ze uniformly distributed within a sphere of radius R. a) Calculate the electric field E for a point inside and outside of the atom at a distance r from the center. b) Derive the electric potential V ( r ) everywhere for this model of atom, by setting V 0 at infinity. ______________________________________________________________________________
Question 4: A thin cylindrical shell of length L and radius R is uniformly charged with total charge Q. a) Find the surface charge density on the shell. b) Find the electric potential at point P which is on the axis of the cylinder, d away from the top. (NOTE: You may find useful some of the integrals given on the first page !)
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Question 5: Consider two long thin concentric cylindrical shells of radius a and b as show in the figure. The shells carry equal and opposite charges per unit length . a) Calculate the electric field and potential for every r<a, a<r<b, r>b. b) Plot the electric field magnitude and the electric potential as a function of r. c) Calculate the capacitance of the structure, per unit length.
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