1. PHYSICS 272 Electric & Magnetic Interactions
Lecture 14
Magnetic Fields [EMI ]

2. 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

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

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

5. 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

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

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

8. Clicker Question 8

9. Clicker Question C 9

10. 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

11. 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

12. 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

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

14. Magnetic monopoles
Electric monopole
Magnetic monopole N S

15. 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

16. 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.

17. 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

18. 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

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

21. 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

22. 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

23. 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

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

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