Exam 1 -- Fall 2005 solutions

Exam 1 -- Fall 2005 solutions - Physics 240 Fall 2005: Exam...

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Physics 240 Fall 2005: Exam #1 Solutions Please print your name:___________________________________________________ Please list your discussion section number:___________________________________ Please list your discussion instructor:________________________________________ Form #1 Instructions 1. Fill in your name above 2. This will be a 1.5 hour, closed book exam. The exam includes 20 questions. 3. You may use a calculator, please do not share calculators 4. You may use one 3”x5” note card with notes and equations you think may be useful. You can write on both sides of the card if you like. 5. You will be asked to show your University student ID card when you turn in your exam. ID checked by:___________________________________ Table of constants: ε 0 = 8.85x10 -12 C 2 /Nm 2 k = 1/(4 πε 0 ) = 8.99x10 9 Nm 2 /C q electron = -1.6x10 -19 C q proton = 1.6x10 -19 C m electron = 9.1x10 -31 kg m proton = 1.67x10 -27 kg G = 6.67x10 -11 Nm 2 /kg 2
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1: Imagine four identical metal spheres; A, B, C, and D. Sphere A has an initial charge of +12Q, sphere B of -14Q, and sphere C of +16Q. The initially neutral sphere D is touched to sphere A, then they are pulled apart. Sphere D is then touched to sphere B, and they are pulled apart. Finally sphere D is touched to sphere C, and they are pulled apart. What is the final charge on sphere D? a) 8Q b) *6Q c) 3.5Q d) -6Q e) 0 2: Consider an infinitely long cylinder with radius R. The cylinder has a uniform charge density ρ (measured in C/m 3 ). What is the magnitude of the electric field at a point r which is inside the cylinder? a) 0 2 ε ρπ r b) * 0 2 ρ r c) 0 d) 0 2 2 r e) 0 2 r R r The idea here is that each time you touch the two identical spheres the divide their charge up equally. So the first time, A and D divide up +12Q, leaving D with +6Q. Then D and B divide up -8Q (-14 + 6), leaving D with -4Q. Then D and C divide up +12Q, leaving D with 6Q. Here you can use Gauss’ law: 0 inside q A d E = ∫∫ r r Choose a surface which is a cylinder of radius r. The electric field points out from the center, and so the electric flux is just 0 ) 2 ( π inside q rL E A d E = = ∫∫ r r The charge inside is the charge density times the volume, so 0 2 0 ) 2 ( L r q rL E inside = = 0 2 r E =
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3: Because charge can flow freely in them, conductors exhibit a variety of special properties. Which of the following statements about conductors in electrostatics is false? a) *The electric potential everywhere inside a conductor must be zero b) The total electric charge on a conductor may be positive or negative c) The electric field inside a conductor is everywhere zero d) Any excess positive or negative charge inside a conductor must be distributed on its surface e) The electric field just outside the conductor is directed perpendicular to its surface 4: The electric field inside a parallel plate capacitor is 5x10 3 N/C. A proton starts out moving perpendicular to this field with a velocity of 3x10
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This note was uploaded on 04/01/2008 for the course PHYSICS 240 taught by Professor Davewinn during the Fall '08 term at University of Michigan.

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Exam 1 -- Fall 2005 solutions - Physics 240 Fall 2005: Exam...

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