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

Info icon This preview shows pages 1–3. Sign up to view the full content.

View Full Document Right Arrow Icon
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
Image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
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 0 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 = 0 ~ E + ~ P = ~ P = ~ D - 0 ~ 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 0 Z b a dr r 2 + q Z c b dr r 2 # = q 4 π 0 1 a - 1 b + 1 κ 1 b - 1 c = C - 1 = 1 4 π 0 1 a - 1 b + 1 κ 1 b - 1 c 2) (30 pts) A azimuthally symmetric charge distribution has charge density in spherical
Image of page 2
Image of page 3
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

What students are saying

  • Left Quote Icon

    As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

    Student Picture

    Kiran Temple University Fox School of Business ‘17, Course Hero Intern

  • Left Quote Icon

    I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

    Student Picture

    Dana University of Pennsylvania ‘17, Course Hero Intern

  • Left Quote Icon

    The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

    Student Picture

    Jill Tulane University ‘16, Course Hero Intern