{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

207_FINALkey_spr11 - Dr Huerta Phy 207 FINAL ANSWER KEY...

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

View Full Document Right Arrow Icon
Dr. Huerta Phy 207 FINAL ANSWER KEY May 10, 2011 Fall 2011, Section HJ, MWF 3:35 – 4:25 p.m. Signature: Name: 1 2 3 4 5 6 ID number: DO PROBLEMS [1.], [2], AND [3.], AND TWO OUT OF PROBLEMS [4], [5.], [6.]. CROSS OUT THE BOX OF THE PROBLEM YOU WILL OMIT Your signature signifies that you will obey the HONOR CODE You may be asked to show your photo ID during the exam. PUT AN X NEXT TO YOUR DISCUSSION SECTION: [ ] Dr. Mezincescu 1O, T 9:30 - 10:20 p.m. [ ] Dr. Alvarez 1Q, T 12:30 - 1:20 p.m. [ ] Dr. Huerta 1R, T 2:00 - 2 :50 p.m. FORMULAE SHEET e = 1 . 6 × 10 - 19 C, m e = 9 . 1 × 10 - 31 kg, m p = 1 . 67 × 10 - 27 kg, k = 1 4 π 0 = 9 × 10 9 N · m 2 C 2 . Coulomb’s Law, Electric Fields (N/C), Electric Field Flux Φ , and Gauss’ Law ~ F = q 1 q 2 4 π 0 r 2 ~ F q = q ~ E, | ~ E Q | = kQ r 2 , Φ closed surface = H ~ E · d ~ A = q inside 0 Electric Field and sheets of surface charge density σ : On each side of an infinite sheet E n = σ 2 0 . However, outside the surface of a conductor, E n = σ 0 . Force, Potential Energy and Torque for an Electric Dipole The Force, torque, and potential energy of an electric dipole ~ p immersed in uniform electric field ~ E are ~ F total = 0 , U = - ~ p · ~ E, ~ τ = ~ p × ~ E. Harmonic Oscillator: F x = - kx , ω = p k/m Electric Potential and Energy : W agent i f = ( K + U ) f - ( K + U ) i , W field i f = U i - U f KE = qV acc , U q ( ~ r ) = qV ( ~ r ) , V i - V f = R f i ~ E · d~s, ~ E = - ∂V ∂x ˆ ı - ∂V ∂y ˆ - ∂V ∂z ˆ k, E r = - ∂V ∂r Capacitance Q = CV, U = Q 2 2 C , u E = 0 E 2 2 , C = κ o A d series 1 C eq = 1 C 1 + 1 C 2 , parallel C eq = C 1 + C 2 Circuits i = R ~ J · ˆ n dA, ~ J = q + n + ~v D + + q - n - ~v D - = σ ~ E, σ = 1 /ρ, V = iR, R = ρL/A Resistors : in series R eq = R 1 + R 2 , in parallel 1 R eq = 1 R 1 + 1 R 2 Kirchhoff’s rules : (1) at a junction, current in equals current out, (2) sum of voltage rises around a loop equals zero. Magnetic forces and Torque : ~ F = q~v × ~ B, ~ F = R i ~ ds × B, ~ τ = μ × ~ B. Physics 207 FINAL May 10, 2011
Image of page 1

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

View Full Document Right Arrow Icon
Dr. Huerta Phy 207 FINAL ANSWER KEY May 10, 2011 Biot-Savart and Ampere-Maxwell laws : d ~ B = μ 0 i 4 πr 3 d~s × ~ r, B = μ 0 i in 2 πr , I C ~ B · ~ ds = μ 0 i in + μ 0 i D = μ 0 Z S ~ J · ˆ n dA + μ 0 0 Z S ~ E ∂t · ˆ n dA Faraday’s Law : E = - d Φ B dt E = H ( ~ E + ~u × ~ B ) · ~ ds, E = - L d i dt , E 2 = - M di 1 dt Self inductance : E = - L di dt . A coil of length , and cross sectional area A , with n turns per unit length has a self inductance L = μ 0 n 2 ‘A . R-C, or R-L circuits : DC charging capacitor with q ( t = 0) = 0 or inductor with i L ( t = 0) = 0 E applied = q C + i C R, q ( t ) = C E applied (1 - e - t/τ C ) , τ C = RC, i C ( t ) = dq dt or E applied = L di L dt + i L R, i L ( t ) = E applied R (1 - e - t/τ L ) , τ L = L/R. Energy in an inductor : U L = 1 2 Li 2 , the energy density in a B field is u B = B 2 2 μ 0 . Angles : sin π 6 = cos π 3 = 1 2 , cos π 6 = sin π 3 = 3 2 , sin π 4 = cos π 4 = 1 2 Complex numbers : i 2 = e = - 1 , i = e i π 2 , z = x + iy = | z | e , | z | = p x 2 + y 2 , tan θ = y x . AC circuits : In a series R-L-C circuit X L = ωL, X C = 1 ωC , Z = Z R + Z L + Z C , where Z R = R , Z L = iX L , Z C = - iX C , Z = | Z | e , | Z | = p R 2 + ( X L - X C ) 2 , tan φ = X L - X C R , and cos φ = R | Z | .
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