Exam 1 Fall 2003 - Physics 171.102 Exam 1 Oct 2 2003 Prof...

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Unformatted text preview: Physics 171.102 Exam 1 Oct. 2, 2003 Prof. Barnett Write your TA’ 5 name and your name on each blue book. Write everything in ink. You may utilize material written on both sides of ONE 3”X 5” index card ASSUME: 7r— — 3.0 1/471'60— — 9 X 109 N7712/C2 p : +25 X 1045 C/m3 1. Assume that a planet is a completely uniform non— rotating sphere with radius RP : 106 m and uniform electr1c charge density p— — +2. 5 x 10 25 C/m3. «(E-RP 6 A) (5 pts) What is the total net electric charge of the planet? 10 m B) (10 pts) What is the electric field, ERP, at the surface of the planet, R 2 RP? C) (10 pts) Explicitly use Gauss’ 3 Law to find the electric field, E (R) inside the planet, i. e. for O < R < RP. Draw a sketch of the magnitude of E versus R for 0 < R < 00. D) (5 pts) Assuming that the electric potential 18 set to 0 at R = 00, what is the electric potential for regions outside the planet, 1. e. Rp < R E) (10 pts) Still assuming that the electric potential is set to 0 at R: 00, find the electric potential for the region inside the planet, ie. R < RP Draw a sketch of the electric potential versus R over the entire region 0 < R < 00. 2. Two capacitors, 01 : IMF and Cg : 2/1F, are connected together as shown in the adjacent figure. The potential at point A is VA 2 0 volts and the potential at point B is 1/3 = 10 volts. VA 2 0 volts B‘ VB : 10 volts. ‘ C2 : 2,111? A) (5 pts) Find the Charge Q1 011 capacitor C1. B) (5 pts) Find the energy stored on capacitor Cl. C) (5 pts 5) Find the value of a capacitor having the same capacitance as the combination of 01 and Cg as shown 1n the figure 1. e. placed between point A and point B. D) (5 pts) A dielectric material with dielectric constant it : 2 is inserted into capacitor Cl. What is the capacitance of 01 after the dielectric is inserted? Y Qq : _10_19 C E) (10 pts) After the dielectric is inserted into 01 what is T g R’3 : 7‘; +5 the potential difference between point A and point B? - _ nanom t 3. Three charges, Q1=+10_19 C Q2 — +1049 C and Q1 2 3.1. " .1,mm+a:e;{s Q3: —10 19 C are located 1n the X— Y plane at R 0,2. + 0 R1— — 01+ Oj, Rg— — i — j, and R3 — 1' +j nanometers 1 T J The particles all have the same mass: 1/11— — 11/12— — Mg Q2 = +1049 C A) (12 pts) What are the forces F12 and E13 of Q1 acting on Q2 and Q3 @ R2 2 Z _3 B) (8 pts) )11/l1at is the electiic dipole moment R2,, of the combination of particles‘Z and 3? C)( (10 pts) )11 hat is the torque 723 on the .1[-) and 113 s1stem about its center of mass? ...
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