PHYS 272 Matter and Interactions II Electric And

PHYS 272: Matter and Interactions II -- Electric And Magnetic Interactions http: //www. physics. purdue. edu/academic_programs/courses/phys 272/ PHYSICS 272 Electric & Magnetic Interactions Lecture 14 Magnetic Fields [EMI 18. 7 -18. 11] Fall 2010 Prof. Yong Chen (yongchen@purdue. edu) Prof. Michael Manfra (mmanfra@purdue. edu) Lec. 12 Slide 1/23

PHYS 272: Matter and Interactions II -- Electric And Magnetic Interactions http: //www. physics. purdue. edu/academic_programs/courses/phys 272/ 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 Fall 2010 Prof. Yong Chen (yongchen@purdue. edu) Prof. Michael Manfra (mmanfra@purdue. edu) Lec. 12 Slide 2/23

PHYS 272: Matter and Interactions II -- Electric And Magnetic Interactions http: //www. physics. purdue. edu/academic_programs/courses/phys 272/ 4. Check the result (4. 1) Check the direction (4. 2) Check the unit (4. 3) When z >> R Fall 2010 Prof. Yong Chen (yongchen@purdue. edu) Prof. Michael Manfra (mmanfra@purdue. edu) Lec. 12 Slide 3/23

PHYS 272: Matter and Interactions II -- Electric And Magnetic Interactions http: //www. physics. purdue. edu/academic_programs/courses/phys 272/ Magnetic Field of a Wire Loop Special case: center of the loop Using general form (z=0) : Fall 2010 Prof. Yong Chen (yongchen@purdue. edu) Prof. Michael Manfra (mmanfra@purdue. edu) Lec. 12 Slide 4/23

PHYS 272: Matter and Interactions II -- Electric And Magnetic Interactions http: //www. physics. purdue. edu/academic_programs/courses/phys 272/ A Coil of Wire What if we had a coil of wire? single loop: For N turns: Fall 2010 Prof. Yong Chen (yongchen@purdue. edu) Prof. Michael Manfra (mmanfra@purdue. edu) Lec. 12 Slide 5/23

PHYS 272: Matter and Interactions II -- Electric And Magnetic Interactions http: //www. physics. purdue. edu/academic_programs/courses/phys 272/ Magnetic Dipole Moment far from coil: magnetic dipole moment: far from dipole: - vector in the direction of B Fall 2010 Prof. Yong Chen (yongchen@purdue. edu) Prof. Michael Manfra (mmanfra@purdue. edu) Lec. 12 Slide 6/23

PHYS 272: Matter and Interactions II -- Electric And Magnetic Interactions http: //www. physics. purdue. edu/academic_programs/courses/phys 272/ Magnetic dipole moment vs. Electric dipole moment Define a vector, , pointing in the direction of the B-field. Fall 2010 Prof. Yong Chen (yongchen@purdue. edu) Prof. Michael Manfra (mmanfra@purdue. edu) Lec. 12 Slide 7/23

PHYS 272: Matter and Interactions II -- Electric And Magnetic Interactions http: //www. physics. purdue. edu/academic_programs/courses/phys 272/ Clicker Question Fall 2010 Prof. Yong Chen (yongchen@purdue. edu) Prof. Michael Manfra (mmanfra@purdue. edu) Lec. 12 Slide 8/23

PHYS 272: Matter and Interactions II -- Electric And Magnetic Interactions http: //www. physics. purdue. edu/academic_programs/courses/phys 272/ Clicker Question C Fall 2010 Prof. Yong Chen (yongchen@purdue. edu) Prof. Michael Manfra (mmanfra@purdue. edu) Lec. 12 Slide 9/23

PHYS 272: Matter and Interactions II -- Electric And Magnetic Interactions http: //www. physics. purdue. edu/academic_programs/courses/phys 272/ The Magnetic Field of a Bar Magnet How does the magnetic field around a bar magnet look like? N S Fall 2010 Prof. Yong Chen (yongchen@purdue. edu) Prof. Michael Manfra (mmanfra@purdue. edu) Lec. 12 Slide 10/23

PHYS 272: Matter and Interactions II -- Electric And Magnetic Interactions http: //www. physics. purdue. edu/academic_programs/courses/phys 272/ Earth as a Magnet Clicker Question 1: Where is earth’s magnetic north pole? A) near geographic north pole (arctic) B) near geographic south pole (Antarctic) C) near equatorial D) near West Lafayette, IN E) not determinable Fall 2010 Prof. Yong Chen (yongchen@purdue. edu) Prof. Michael Manfra (mmanfra@purdue. edu) Lec. 12 Slide 11/23

PHYS 272: Matter and Interactions II -- Electric And Magnetic Interactions http: //www. physics. purdue. edu/academic_programs/courses/phys 272/ Earth as a Magnet N S Clicker Question 1: Where is earth’s magnetic north pole? A) near geographic north pole (arctic) B) near geographic south pole (Antarctic) C) near equatorial D) near West Lafayette, IN E) not determinable B Fall 2010 Prof. Yong Chen (yongchen@purdue. edu) Prof. Michael Manfra (mmanfra@purdue. edu) Lec. 12 Slide 12/23

PHYS 272: Matter and Interactions II -- Electric And Magnetic Interactions http: //www. physics. purdue. edu/academic_programs/courses/phys 272/ The Magnetic Field of Earth Surface “north” component of magnetic field depends on latitude B Maine: ~1. 5. 10 -5 T Indiana: ~2. 10 -5 T Florida: ~3. 10 -5 T Fall 2010 Prof. Yong Chen (yongchen@purdue. edu) Prof. Michael Manfra (mmanfra@purdue. edu) Lec. 12 Slide 13/23

PHYS 272: Matter and Interactions II -- Electric And Magnetic Interactions http: //www. physics. purdue. edu/academic_programs/courses/phys 272/ Magnetic monopoles Electric monopole N Magnetic monopole S Fall 2010 Prof. Yong Chen (yongchen@purdue. edu) Prof. Michael Manfra (mmanfra@purdue. edu) Lec. 12 Slide 14/23

PHYS 272: Matter and Interactions II -- Electric And Magnetic Interactions http: //www. physics. purdue. edu/academic_programs/courses/phys 272/ Twisting of a Magnetic Dipole 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. Fall 2010 Prof. Yong Chen (yongchen@purdue. edu) Prof. Michael Manfra (mmanfra@purdue. edu) Lec. 12 Slide 15/23

PHYS 272: Matter and Interactions II -- Electric And Magnetic Interactions http: //www. physics. purdue. edu/academic_programs/courses/phys 272/ A single atom can be a magnetic dipole Three possibilities for the source of magnetic dipole moment: (1)An electron orbiting around the nucleus; (2)An electron spinning on its own axis; (3)Rotational motion in the nucleus where μ is the magnetic dipole moment and L is the angular momentum. Fall 2010 Prof. Yong Chen (yongchen@purdue. edu) Prof. Michael Manfra (mmanfra@purdue. edu) Lec. 12 Slide 16/23

PHYS 272: Matter and Interactions II -- Electric And Magnetic Interactions http: //www. physics. purdue. edu/academic_programs/courses/phys 272/ Magnetic dipole moment of an orbiting electron where R is the orbital radius and v is the speed of the electron. For angular momentum where p is the momentum. quantum Fall 2010 Prof. Yong Chen (yongchen@purdue. edu) Prof. Michael Manfra (mmanfra@purdue. edu) Lec. 12 Slide 17/23

PHYS 272: Matter and Interactions II -- Electric And Magnetic Interactions http: //www. physics. purdue. edu/academic_programs/courses/phys 272/ Spinning electron or nucleons Assuming the same expression For an electron: For a nucleon: Conclusion: Only consider electron spin and electron orbital contribution Assuming L = ħ Fall 2010 Prof. Yong Chen (yongchen@purdue. edu) Prof. Michael Manfra (mmanfra@purdue. edu) Lec. 12 Slide 18/23

PHYS 272: Matter and Interactions II -- Electric And Magnetic Interactions http: //www. physics. purdue. edu/academic_programs/courses/phys 272/ Fall 2010 Prof. Yong Chen (yongchen@purdue. edu) Prof. Michael Manfra (mmanfra@purdue. edu) Lec. 12 Slide 19/23

PHYS 272: Matter and Interactions II -- Electric And Magnetic Interactions http: //www. physics. purdue. edu/academic_programs/courses/phys 272/ Alignment of the atomic magnetic dipole moments Biron = 0 Biron Bcoil Application: Electromagnet Fall 2010 Prof. Yong Chen (yongchen@purdue. edu) Prof. Michael Manfra (mmanfra@purdue. edu) Lec. 12 Slide 20/23

PHYS 272: Matter and Interactions II -- Electric And Magnetic Interactions http: //www. physics. purdue. edu/academic_programs/courses/phys 272/ Example: A compass originally points north. A bar magnet whose mass is 69. 5 g is aligned east-west and placed near the compass as shown in the right figure. When the distance between the center of the magnet and the center of the compass is 23. 3 cm, the compass deflects 70 degrees. What is the magnetic dipole moment of the bar magnet? Earth magnetic field: 2× 10 -5 T Fall 2010 Prof. Yong Chen (yongchen@purdue. edu) Prof. Michael Manfra (mmanfra@purdue. edu) Lec. 12 Slide 21/23

PHYS 272: Matter and Interactions II -- Electric And Magnetic Interactions http: //www. physics. purdue. edu/academic_programs/courses/phys 272/ Example: A compass originally points north. A bar magnet whose mass is 69. 5 g is aligned east-west and placed near the compass as shown in the right figure. When the distance between the center of the magnet and the center of the compass is 23. 3 cm, the compass deflects 70 degrees. What is the magnetic dipole moment of the bar magnet? Earth magnetic field: 2× 10 -5 T Fall 2010 Prof. Yong Chen (yongchen@purdue. edu) Prof. Michael Manfra (mmanfra@purdue. edu) Lec. 12 Slide 22/23

PHYS 272: Matter and Interactions II -- Electric And Magnetic Interactions http: //www. physics. purdue. edu/academic_programs/courses/phys 272/ Example: A compass originally points north. A bar magnet whose mass is 69. 5 g is aligned east-west and placed near the compass as shown in the right figure. When the distance between the center of the magnet and the center of the compass is 23. 3 cm, the compass deflects 70 degrees. What is the magnetic dipole moment of the bar magnet? Earth magnetic field: 2× 10 -5 T Assume that almost all of the atoms in this magnet are iron atoms. The mass of one mole of iron is 56 g. order of magnitude right Fall 2010 Prof. Yong Chen (yongchen@purdue. edu) Prof. Michael Manfra (mmanfra@purdue. edu) Lec. 12 Slide 23/23

PHYS 272: Matter and Interactions II -- Electric And Magnetic Interactions http: //www. physics. purdue. edu/academic_programs/courses/phys 272/ Food for thought: Nuclear Magnetic Resonance (NMR) Proton spin Magnet N S Felix Bloch (1905 -1983) 1952 Edward Purcell (BSEE’ 33) (1912 -1997) B field Fall 2010 Prof. Yong Chen (yongchen@purdue. edu) Prof. Michael Manfra (mmanfra@purdue. edu) Lec. 12 Slide 24/23

PHYS 272: Matter and Interactions II -- Electric And Magnetic Interactions http: //www. physics. purdue. edu/academic_programs/courses/phys 272/ Re. Cap • Magnetic Field of Current Loop • Magnetic Dipole Moment • Magnetic Dipole: electrons, protons, atoms, matter… Fall 2010 Prof. Yong Chen (yongchen@purdue. edu) Prof. Michael Manfra (mmanfra@purdue. edu) Lec. 12 Slide 25/23