PHYSICS 272 Electric & Magnetic Interactions Lecture 14 Magnetic Fields [EMI 18.7-18.11]

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

Check the result (4.1) Check the direction (4.2) Check the unit (4.3) When z >> R

Magnetic Field of a Wire Loop Special case: center of the loop Using general form (z=0) : 4

A Coil of Wire What if we had a coil of wire? single loop: For N turns: Make a usual coil – and then with loops running in opposite directions. 5

Magnetic Dipole Moment far from coil: far from dipole: magnetic dipole moment:  - vector in the direction of B 6

Magnetic dipole moment vs. Electric dipole moment Define a vector, , pointing in the direction of the B-field.

Clicker Question 8

Clicker Question C 9

The Magnetic Field of a Bar Magnet How does the magnetic field around a bar magnet look like? N S Do experiment with compass and bar magnet to figure out. 10

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 Do experiment with compass and bar magnet to figure out. 11

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 Do experiment with compass and bar magnet to figure out. B 12

The Magnetic Field of Earth Surface “north” component of magnetic field depends on latitude Maine: ~1.5.10-5 T Indiana: ~2.10-5 T Florida: ~3.10-5 T Do experiment with compass and bar magnet to figure out. B 13

Magnetic monopoles Electric monopole Magnetic monopole N S

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. 15

A single atom can be a magnetic dipole Three possibilities for the source of magnetic dipole moment: An electron orbiting around the nucleus; An electron spinning on its own axis; Rotational motion in the nucleus where μ is the magnetic dipole moment and L is the angular momentum.

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

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

Alignment of the atomic magnetic dipole moments Biron Biron = 0 Bcoil Application: Electromagnet

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

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

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

Nuclear Magnetic Resonance (NMR) Food for thought: S N Proton spin Magnet Felix Bloch (1905 -1983) Edward Purcell (BSEE’33) (1912-1997) 1952 B field 24

ReCap Magnetic Field of Current Loop Magnetic Dipole Moment Magnetic Dipole: electrons, protons, atoms, matter…