1. Fall 2010 Prof. Yong Chen (yongchen@purdue.edu) Prof. Michael Manfra (mmanfra@purdue.edu) Lecture 10 Slide 1yongchen@purdue.edummanfra@purdue.edu PHYS 272: Matter and Interactions II -- Electric And Magnetic Interactions http://www.physics.purdue.edu/academic_programs/courses/phys272/ PHYSICS 272 Electric & Magnetic Interactions Lecture 12 Magnetic Fields [EMI 18.5-18.7]

2. Fall 2010 Prof. Yong Chen (yongchen@purdue.edu) Prof. Michael Manfra (mmanfra@purdue.edu) Lecture 10 Slide 2yongchen@purdue.edummanfra@purdue.edu PHYS 272: Matter and Interactions II -- Electric And Magnetic Interactions http://www.physics.purdue.edu/academic_programs/courses/phys272/ Conclusions: The magnitude of B depends on the amount of current A wire with no current produces no B B is perpendicular to the direction of current B under the wire is opposite to B over the wire Oersted effect: discovered in 1820 by H. Ch. Ørsted How does the field around a wire look like? The Magnetic Effects of Currents

3. Fall 2010 Prof. Yong Chen (yongchen@purdue.edu) Prof. Michael Manfra (mmanfra@purdue.edu) Lecture 10 Slide 3yongchen@purdue.edummanfra@purdue.edu PHYS 272: Matter and Interactions II -- Electric And Magnetic Interactions http://www.physics.purdue.edu/academic_programs/courses/phys272/ Principle of superposition: What can you say about the magnitudes of B Earth and B wire ? What if B Earth were much larger than B wire ? The Magnetic Effects of Currents The moving electrons in a wire create a magnetic field

4. Fall 2010 Prof. Yong Chen (yongchen@purdue.edu) Prof. Michael Manfra (mmanfra@purdue.edu) Lecture 10 Slide 4yongchen@purdue.edummanfra@purdue.edu PHYS 272: Matter and Interactions II -- Electric And Magnetic Interactions http://www.physics.purdue.edu/academic_programs/courses/phys272/ A current-carrying wire is oriented N-S and laid on top of a compass. The compass needle points 27 o west. What is the magnitude and direction of the magnetic field created by the wire B wire if the magnetic field of Earth is B Earth = 2   10 -5 T (tesla). Exercise

5. Fall 2010 Prof. Yong Chen (yongchen@purdue.edu) Prof. Michael Manfra (mmanfra@purdue.edu) Lecture 10 Slide 5yongchen@purdue.edummanfra@purdue.edu PHYS 272: Matter and Interactions II -- Electric And Magnetic Interactions http://www.physics.purdue.edu/academic_programs/courses/phys272/ Electron current vs. conventional current where n is the mobile electron density, A is the cross-sectional area of wire, is the average drift speed of electrons, and in a metal. Number of electrons? Number of electrons per secondCoulombs per second, or Amperes Electron current Conventional current

6. Fall 2010 Prof. Yong Chen (yongchen@purdue.edu) Prof. Michael Manfra (mmanfra@purdue.edu) Lecture 10 Slide 6yongchen@purdue.edummanfra@purdue.edu PHYS 272: Matter and Interactions II -- Electric And Magnetic Interactions http://www.physics.purdue.edu/academic_programs/courses/phys272/ Typical electron current in a circuit is ~ 10 18 electrons/s. What is the drift speed of an electron in a 1 mm thick copper wire of circular cross section? Typical Mobile Electron Drift Speed

7. Fall 2010 Prof. Yong Chen (yongchen@purdue.edu) Prof. Michael Manfra (mmanfra@purdue.edu) Lecture 10 Slide 7yongchen@purdue.edummanfra@purdue.edu PHYS 272: Matter and Interactions II -- Electric And Magnetic Interactions http://www.physics.purdue.edu/academic_programs/courses/phys272/ Metals: current consists of electrons Semiconductors: n-type – electrons p-type – positive holes conventional current: Conventional Current Units: C/s  A (Ampere) In some materials current moving charges are positive: Ionic solution “Holes” in some materials (same charge as electron but +) Observing magnetic field around copper wire: Can we tell whether the current consists of electrons or positive ‘holes’? The prediction of the Biot-Savart law is exactly the same in either case.

8. Fall 2010 Prof. Yong Chen (yongchen@purdue.edu) Prof. Michael Manfra (mmanfra@purdue.edu) Lecture 10 Slide 8yongchen@purdue.edummanfra@purdue.edu PHYS 272: Matter and Interactions II -- Electric And Magnetic Interactions http://www.physics.purdue.edu/academic_programs/courses/phys272/ Why? See next page.

9. Fall 2010 Prof. Yong Chen (yongchen@purdue.edu) Prof. Michael Manfra (mmanfra@purdue.edu) Lecture 10 Slide 9yongchen@purdue.edummanfra@purdue.edu PHYS 272: Matter and Interactions II -- Electric And Magnetic Interactions http://www.physics.purdue.edu/academic_programs/courses/phys272/ Formula for one moving charge Sum all the moving charges in the short segment of wire Total number of moving charges RecallTherefore

10. Fall 2010 Prof. Yong Chen (yongchen@purdue.edu) Prof. Michael Manfra (mmanfra@purdue.edu) Lecture 10 Slide 10yongchen@purdue.edummanfra@purdue.edu PHYS 272: Matter and Interactions II -- Electric And Magnetic Interactions http://www.physics.purdue.edu/academic_programs/courses/phys272/ x y Superposition Principle  Magnetic Field for a extended current (straight wire)

11. Fall 2010 Prof. Yong Chen (yongchen@purdue.edu) Prof. Michael Manfra (mmanfra@purdue.edu) Lecture 10 Slide 11yongchen@purdue.edummanfra@purdue.edu PHYS 272: Matter and Interactions II -- Electric And Magnetic Interactions http://www.physics.purdue.edu/academic_programs/courses/phys272/

12. Fall 2010 Prof. Yong Chen (yongchen@purdue.edu) Prof. Michael Manfra (mmanfra@purdue.edu) Lecture 10 Slide 12yongchen@purdue.edummanfra@purdue.edu PHYS 272: Matter and Interactions II -- Electric And Magnetic Interactions http://www.physics.purdue.edu/academic_programs/courses/phys272/ Clicker Question 1 Current carrying wires below lie in X-Y plane.

13. Fall 2010 Prof. Yong Chen (yongchen@purdue.edu) Prof. Michael Manfra (mmanfra@purdue.edu) Lecture 10 Slide 13yongchen@purdue.edummanfra@purdue.edu PHYS 272: Matter and Interactions II -- Electric And Magnetic Interactions http://www.physics.purdue.edu/academic_programs/courses/phys272/ Clicker Question 1 Current carrying wires below lie in X-Y plane. C

14. Fall 2010 Prof. Yong Chen (yongchen@purdue.edu) Prof. Michael Manfra (mmanfra@purdue.edu) Lecture 10 Slide 14yongchen@purdue.edummanfra@purdue.edu PHYS 272: Matter and Interactions II -- Electric And Magnetic Interactions http://www.physics.purdue.edu/academic_programs/courses/phys272/ Four-step approach: 1.Cut up the current distribution into pieces and draw  B 2.Write an expression for  B due to one piece 3.Add up the contributions of all the pieces 4.Check the result Magnetic Field of Current Distributions

15. Fall 2010 Prof. Yong Chen (yongchen@purdue.edu) Prof. Michael Manfra (mmanfra@purdue.edu) Lecture 10 Slide 15yongchen@purdue.edummanfra@purdue.edu PHYS 272: Matter and Interactions II -- Electric And Magnetic Interactions http://www.physics.purdue.edu/academic_programs/courses/phys272/ 1.Draw ∆B for an arbitrary piece 2.Write an expression for ∆B (2.1) Direction: Right-hand rule ∆B  got cancelled out; only consider ∆B z (2.2) Magnitude:

16. Fall 2010 Prof. Yong Chen (yongchen@purdue.edu) Prof. Michael Manfra (mmanfra@purdue.edu) Lecture 10 Slide 16yongchen@purdue.edummanfra@purdue.edu PHYS 272: Matter and Interactions II -- Electric And Magnetic Interactions http://www.physics.purdue.edu/academic_programs/courses/phys272/ 3.Add up all the pieces Direction of B-field is along the z-axis (right-hand rule for loops) Recall E-field of a ring

17. Fall 2010 Prof. Yong Chen (yongchen@purdue.edu) Prof. Michael Manfra (mmanfra@purdue.edu) Lecture 10 Slide 17yongchen@purdue.edummanfra@purdue.edu PHYS 272: Matter and Interactions II -- Electric And Magnetic Interactions http://www.physics.purdue.edu/academic_programs/courses/phys272/ What if we had a coil of wire? For N turns: single loop: A Coil of Wire

18. Fall 2010 Prof. Yong Chen (yongchen@purdue.edu) Prof. Michael Manfra (mmanfra@purdue.edu) Lecture 10 Slide 18yongchen@purdue.edummanfra@purdue.edu PHYS 272: Matter and Interactions II -- Electric And Magnetic Interactions http://www.physics.purdue.edu/academic_programs/courses/phys272/ Magnetic dipole moment vs. Electric dipole moment Define a vector,, pointing in the direction of the B-field.

19. Fall 2010 Prof. Yong Chen (yongchen@purdue.edu) Prof. Michael Manfra (mmanfra@purdue.edu) Lecture 10 Slide 19yongchen@purdue.edummanfra@purdue.edu PHYS 272: Matter and Interactions II -- Electric And Magnetic Interactions http://www.physics.purdue.edu/academic_programs/courses/phys272/ far from coil:far from dipole: magnetic dipole moment:  - vector in the direction of B Magnetic Dipole Moment

20. Fall 2010 Prof. Yong Chen (yongchen@purdue.edu) Prof. Michael Manfra (mmanfra@purdue.edu) Lecture 10 Slide 20yongchen@purdue.edummanfra@purdue.edu PHYS 272: Matter and Interactions II -- Electric And Magnetic Interactions http://www.physics.purdue.edu/academic_programs/courses/phys272/ Clicker Question 2

21. Fall 2010 Prof. Yong Chen (yongchen@purdue.edu) Prof. Michael Manfra (mmanfra@purdue.edu) Lecture 10 Slide 21yongchen@purdue.edummanfra@purdue.edu PHYS 272: Matter and Interactions II -- Electric And Magnetic Interactions http://www.physics.purdue.edu/academic_programs/courses/phys272/ Clicker Question 2 C

22. Fall 2010 Prof. Yong Chen (yongchen@purdue.edu) Prof. Michael Manfra (mmanfra@purdue.edu) Lecture 10 Slide 22yongchen@purdue.edummanfra@purdue.edu PHYS 272: Matter and Interactions II -- Electric And Magnetic Interactions http://www.physics.purdue.edu/academic_programs/courses/phys272/ The magnetic dipole moment  acts like a compass needle! In the presence of external magnetic field a current-carrying loop rotates to align the magnetic dipole moment  along the field B. Twisting of a Magnetic Dipole