Physics 202, Lecture 14

Transcription

1 Physics 202, Lecture 14 Today s Topics Sources of the Magnetic Field (Ch 30) Review: The Biot-Savart Law The Ampere s Law Applications And Exercises of ampere s Law Straight line, Loop, Solenoid, Toroid Magnetism in Matter

2 About Exam 2 When and where Friday March. 13 th 5:30-7:00 pm 2650, 3650 Humanities (same as exam 1 ) Format Closed book 1+1 8x11 formula sheet allowed, must be self prepared, no photo copy of solutions, no photo copy of lecture slides. Four full problems. (~20 questions) Bring a calculator (but no computer). Only basic calculation functionality can be used. Special Arrangements: e All alternative time tests must be preapproved. No early test before Friday Mar 13 th possible. Alternative test available in earlier afternoon (~ 4pm) in lab rooms (for approved requests only)

3 Review Sessions There will be two identical review sessions: Saturday, March 7 th, 2-4 pm Sunday, March 8 th, 7-9 pm Both are in 2103 Chamberlin. (this room) Each session = ~70 min lecturing + Q&A

4 Ampere s Law: Review: Ampere s Law r I B ds = μ0i closed any path It applies to any closed path It applies to any static B field It is practically useful only in symmetric cases ds Ampere s Law can be derived from Biot-Savart Law It has also a generalized form: Ampere-Maxwell law (later in the lecture)

5 Exercise: Solenoid The B field inside an ideal solenoid is: B = μ0ni n=n/l idea solenoid segment 3 at

6 Compare Solenoid and Bar Magnet N S Loose Solenoid Tight Solenoid Bar Magnet B I

7 Exercise: Toroid (Text example 30.5) Show the B field inside a toroid is: hint: Use Ampere s Law (See board) B = μ 0 NI 2πr

8 Review: Electric Dipole Moments Electric dipole moment p. -q - p= qd F = 0 +q r + τ = p E U = -p E Dielectric material contains electric dipoles at atomic level In an external field E 0, the dipoles line up E ind is always opposite to E 0 E=E 0 /κ<e 0, C=κC 0 (dielectric constant κ>1)

9 Review: Magnetic Dipole Moments Magnetic dipole moment μ. Note: B produced (at the center) is always in same direction as μ μ B Macroscopic μ=ia Microscopic μ L angular momentum of orbiting or spin definition of magnetic moment F = 0 r v τ = μ B r U = - μ B μ in B Field

10 Magnetism in Matter Induced dfield ldb ind in response to an external B 0 : B ind = χbb 0 the net field inside: B = B 0 +B ind =(1+χ) B 0 = (μ m /μ 0 )B 0 μ m : magnetic permeability, χ: magnetic susceptibility Classification of Magnetic Matter χ=μ 0 Type Direction of Strength of m /μ -1 Contributing B induced B induced Elements Ferromagnetic Same as B 0 Strong >>0 Domain of (e.g. Fe, Co, Ni ) (~10 3 ) Magnetic Dipole Paramagnetic Same as B 0 Weak >0 μ atoms (e.g. Al, Ca, ) (~10-5 ) Diamagnetic (e.g. Cu, Au, ) Opposite Weak <0 (~-10-5 ) Magnetic Quadruple Superconductor Opposite =-B 0-1 Quantum eff.

11 Permanent Magnetic Moments (domains) Inside Ferromagnetic Material polarized domains No external B field, B 0 applied, permanent permanent mag. moments magnetic moments line up exist, but oriented randomly in the direction of B 0 no induced d B field strong induced d B field Note: Inductance with a ferromagnetic core: L= μ m /μ 0 L 0 >>L 0

12 Demo: Meissner Effect Certain superconductors (type I) exhibit perfect diamagnetism in superconducting state: no magnetic field allowed inside (Meissner Effect)