p240_ct3_f07 - Physics 240 Fall 2007 Lecture #3 Student...

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Physics 240 Fall 2007 Lecture #3 Dr. Dave Winn 2405 Randall Lab winn@umich.edu Student Physics Society Mass Meeting: Tonight 9/11/07 at 7:00 in West Hall 337 (Free Pizza, non-majors welcome)
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Coulomb’s law, point charges, and the attraction of neutral objects • Coulomb’s law applies to point charges only . • Forces on extended objects are calculated by superposition: by adding up the Coulomb forces among all the point charges in the problem. • Force between any point charge and a neutral point object is zero • Force between a charge and an extended neutral object comes from induced charge separation.
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+ charge No net charge No force! + charge No net charge _ _ _ + + + Charge separation allows net attraction! Big force Smaller force Neutral extended objects are attracted, neutral point objects feel no force.
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Electrostatic shell theorems • Note similarity between Coulomb force and Newtonian gravity: • Gravity always attractive, electrostatic attractive or repulsive 1. Uniform shell of charge attracts or repels as if all charge sits at the center 2. A uniform shell of charge exerts no force on a charged particle inside the shell Both follow from 1/r 2 force law! Applies less often in E&M because charge can move. .. G Fk QQ r r Coulomb = 12 2 ± G F Gm m r r Gravity =− 12 2 ±
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A uniformly charged sphere has a radius R and a total charge Q. A point charge q is placed at a distance r=R/2 from the center of the sphere. What is the magnitude of the Coulomb force felt by the point charge? What is | F q |?
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A uniformly charged sphere has a radius R and a total charge Q. A point charge q is placed at a distance r=R/2 from the center of the sphere. What is the magnitude of the Coulomb force felt by the point charge? The force depends only on that charge which is interior to r. The total charge in there is: Q in = Q/(4/3 π R 3 ) * 4/3 π r 3 = Q/R 3 *(R/2) 3 = Q/8 The force is then: F = kqQ in /r 2 = kqQ/8r 2 = kqQ/8(R/2) 2 = (1/2)kqQ/R 2 | F q | = (1/2)kqQ/R 2
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The situation is the same as in the last question, except now a sub-sphere of Q has been hollowed out around q, leaving a gap. What is the force experienced by the point charge now?
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p240_ct3_f07 - Physics 240 Fall 2007 Lecture #3 Student...

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