mt1_solution

mt1_solution - Physics 501—Fall 2011 Midterm Name...

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Unformatted text preview: Physics 501—Fall 2011 Midterm Name: Instructions: • This is an in-class closed book exam. You will find a set of potentially useful formulas at the back of the exam. • There are three problems, whose weights are indicated. • Partial credit will be given provided your work is shown and can be understood. • Undergrads: Be sure to write and sign the pledge in the exam booklet: “I pledge my honor that I have not violated the Honor Code during this examination.” 1 c a κ b 1) (30 pts) The gap between two concentric con- ducting spherical shells having radius a and c is par- tially filled by a concentric spherical shell dielectric of inner radius b and outer radius c . The dielectric constant of the material between b and c is κ . The region between a and b is vacuum. A charge q resides on the surface of the inner conducting sphere. a) Find the electric field ~ E ( ~ r ) in the region a < r < b . Solution: ~ E = q 4 π r 2 ˆ r b) Find the electric field ~ E ( ~ r ) and the polarization ~ P ( ~ r ) in the region b < r < c . Solution: ~ D = q 4 πr 2 ˆ r = ~ E = ~ E + ~ P = ⇒ ~ P = ~ D- ~ E = 1- 1 κ ~ D = 1- 1 κ q 4 πr 2 ˆ r c) Find the capacitance between the inner and outer conducting shells. Solution: C = q V V = Z b a ~ E · d ~ dr + Z c b ~ E · d ~ dr = q 4 π " 1 Z b a dr r 2 + q Z c b dr r 2 # = q 4 π 1 a- 1 b + 1 κ 1 b- 1 c = ⇒ C- 1 = 1 4 π 1 a...
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This note was uploaded on 02/04/2012 for the course PHY 501 at Princeton.

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mt1_solution - Physics 501—Fall 2011 Midterm Name...

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