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Exam 1 Spring 2002 - "ix 1 1 Physics 171.102 Exam 1...

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Unformatted text preview: "ix 1 1 Physics 171.102 Exam 1 February 26, 2002 Prof. Barnett Write your TA’s name, your name and Section Number on each blue book. Write everything in ink. You may utilize material written on both sides of ONE 3”x5” index card. 60 = 8.9 x 10—12N9‘m2 a = 9 x 109 N592 g = 10 m/s2 1. Two tiny conducting balls of identical mass m and identical charge q hang from non—conducting massless threads of length L on earth as shown in the figure. The angle 6 is so small that tan(6) can be approximated as sin(6) if this is convenient. lea.-- \' __,1 A) (10 pts) What are the forces Fl acting on the right hand mass? B) (10 pts) Find the formula relating q to the other relevant parameters (L, m, :13) in the problem. C) (10 pts) If L : 120 cm, m z 10 grams and :1: = 5 cm, what is q? 2. The adjacent figure shows a cross section of a if“ 2‘ neutrally charged (uncharged) spherical metal "(X/120 shell of inner radius RI and outer radius R0. %. . R 2 A point charge of Q 2 —9 MO is located a -.~, I/ distance R1/2 from the center of the spherical shell. A) (5 pts) What is the total induced charge on the inner surface of the spherical shell? Is this charge spread uniformly on the surface? B) (5 pts) What is the total induced charge on the outer surface of the spherical shell? Is this charge spread uniformly on the surface? C) (5 pts) What is the electric field EU?) inside the material of the shell, i.e. for R] < R < R0? D) (10 pts) What is the electric field E(R) outside the spherical shell, i.e. for R > R0? E) (5 pts) If the charge Q : ~9 ,LLC were located at the center of the sphere instead of at R : RI/ 2 how would the electric field E(R) outside the spherical shell, i.e. R > R0, change? 3. A capacitor consists of two oppositely charged flat parallel plates. Each plate has a square shape with edges of length 10 cm. One plate has charge 62+ 2 9 X 10~10 C and the other plate has charge Q_ = —9 X 10—10 C. The plates are 1 mm apart. A) (10 pts) What is the potential difference across the capacitor? B) (10 pts) If an electron with charge 6 = ——l.6 X 10‘19 C and mass m = 9 X 10"31 kg is released at rest from the surface of the negatively charged plate how much time passes before it collides with the positively charged plate? ' C) (10 pts) What is the kinetic energy of this electron when it collides with the positive plate? 4. The electric potential at the point P ‘P in the adjacent figure due to a uniform 1 charge density /\ on a uniform rod ' of length L is given by lH;L———>l—_x _ A L+§L2+d2)1/2 V(d) _. 4m) m( d j. A) (5 pts) What is the potential at the P point P in the adjacent figure showing j an identical rod of length L except that d it is split into a right and left half and where the left and right halves have the PM fiL—m 4 same linear charge density A. B) (5 pts) What is the potential at the point P in the adjacent figure again p showing an identical rod split into two i halves, but this time with the linear charge densities being +)\ for the “Em"‘mgfl‘ma left half and —A for the right half? ...
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