Magnetism

Diamagnetic materials M = χH

CS: 30.10

B = (1 + χ ) µ 0 H

Susceptibility is small (weak) and negative: χ < 0 → µ < µ0.

Linear response (χ independent of H): no permanent M when H = 0.

Susceptibility (χ) smaller at high-T due to thermal disorder.

All materials are weakly diamagnetic if they lack atomic moments. When moments are present, diamagnetism isn’t noticeable.

Weakly repelled from a magnetic field.

http://www.physics.ucla.edu/marty/diamag/

Note on

Monday is fee late day.

iClicker Quiz: 30:6 I have completed at least 50% of the reading and study-guide assignments associated with the lecture, as indicated on the course schedule. A. True B. False Today: use your Chapter Summaries. Review; 3 kinds of magnetism: Dia-, para-, & ferromagnetism; 3) Magnetization curves & Curie’s law; Hint: The exam runs Wednesday 2 Nov. 4 pm until Saturday 5 November plus Monday Nov. 7 all day is a fee late day. (If you need to take the exam BEFORE 4pm today, see me.

36 MC questions and 3 HWS problems. 4 pages!

Remember that Curie’s Law & Curie’s temperature are for different phenomena!

T/F (A/B) In diamagnetism the magnetism field is strengthened inside the material.

The proper order of strength of these effects, from weakest to strongest, a. paramagnetism b. diamagnetism c. ferromagnetism is the following: A. a,b,c D. b c a B. a c b E. c b a F. c a b C. b a c

The Meissner effect for YBa2Cu3O7 Permanent magnet

Perfect diamagnetism: χ = −1 B = (1 + χ ) µ 0 H = (1 − 1) µ 0 H = 0

Superconductor (T < Tc) When fields from the magnet attempt to enter the SC material, surface currents in the SC do whatever it takes to create exactly the opposite field. The magnet levitates in the opposing fields from the SC.

Paramagnetic materials M = χH

B = (1 + χ ) µ 0 H

CS: 30.11

Susceptibility is small (weak) & positive: χ > 0 → µ > µ0.

Linear response (χ independent of H): no permanent M when H = 0.

Susceptibility decreases at high-T due to thermal disorder. Curie’s law: M ∝ B/T. The constant of proportionality is called the Curie Constant.

All materials with nonzero atomic moments are paramagnetic at high T. Weakly attracted to a magnetic field

Is the material in 23-1 A. Diamagnetic B. Paramagnetic C. Something else?

Why?

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1/ 2

Above Curie temperature a ferromagnetic material becomes paramagnetic.

CS: 30.9

Ferromagnetic materials

T −T   M 0  C T  C 

Ferromagnetic materials Domain structure: Explains permanently magnetized materials

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T −T   M 0  C T  C 

Above Curie temperature a ferromagnetic material becomes paramagnetic.

Ferromagnetic materials M = χH

B = (1 + χ ) µ 0 H

Susceptibility is very large & positive: χ >> 0 →

µ >> µ0.

Nonlinear response (χ depends on H and past history) – hysteresis.

(χ can be a matrix.)

Paramagnetic above Curie temperature (TC).

Spontaneous moment (at H = 0) below TC.

Moments aligned within magnetic domains, but domains can be disordered. External field can causes domains to align & grow or shrink. .

Strongly attracted to a magnetic field www.wikipedia.org

Hysteresis in ferromagnets Saturation Remanence

Coercitivity

Good permanent magnets need both high remanence and high coercitivity (loop area determines the ability to do magnetic work).

Hard ferromagnet

Soft ferromagnet

Iron (Fe) is magnetically soft (small Hc). NdFeB is â&#x20AC;&#x153;hardâ&#x20AC;? (large Hc).

non-magnetic

diamagnetic

paramagnetic

ferromagnetic

χ =0

χ <0

χ >0

χ >> 0

hysteresis

µ = µ0

µ < µ0

µ > µ0

µ >> µ 0

hysteresis

No real material (except the vacuum) is non-magnetic

no atomic moments needed at H = 0

requires atomic moments at H = 0

weaker at high T

Curie’s law

weakly repelled by magnetic fields

weakly attracted to magnetic fields

permanent (H = 0) magnetic domains below TC strongly attracted to magnetic fields hard or soft

1. You will need to know how a cathode ray tube (an old fashion TV) works.

2. (Motion of electrons in a magnetic field.)

3. Hall effect type problems 4. Problems: voltage due to water flowing in a river.

5. Ampere & Gaussâ&#x20AC;&#x2122;s law problems.

29.15

The Provo River near Utah Lake runs from east to west while the earth's magnetic field has downward & northward components. Assume that the river is electrically neutral, but contains dissolved positive & negative ions in equal amounts. Assume also that the ions move at the same speed as the water in the river. The north bank of the river has an electrical potential that is (A) higher (B) lower (C) the same as the potential of the south bank.

Which of these trajectories belongs to the fastest charged particle? 1 & 6 are A, 2 & 7 are B etc.

Assume all are same mass and magnitude of charge.

The magnetic flux through each of 5 faces of a die (singular of dice) numbered 2 through 6 has a magnitude N x 10-9 Wb where â&#x20AC;&#x153;N" is the number of spots on that face (2 through 6).

This flux is outward (positive) for N even and inward (negative) for N odd. The magnitude of the net flux through the face with one spot is _____Wb. (report 1st digit when number is in Scientific Notation. )

A is 1&6, B is 2&7, C is â&#x20AC;Ś