1. PHYSICS 272 Electric & Magnetic Interactions
Lecture 21
Magnetic Force [Chap. 21]
Field Lines/Pattern in Space [Chap 22] –Gauss Law

2. Lowest energy   = 0

3. Force on a magnetic dipole
Like currents attract
Direction: Attractive
Magnitude: Need 

4. Force on a magnetic dipole1 2
Magnitude: Need B-field distribution
Direction: Attractive

5. Force on a Magnetic Dipole
Two magnets
Negative sign indicates that F due to magnet is such as to draw loop towards the magnet. 5

6. Bar magnet is equivalent
to a magnetic dipole
Silver atoms

7. Demo of Quantum Mechanics
What we know:
(a) Each silver atom has angular momentum and a magnetic dipole momentum
(b) Silver atoms should experience a vertical force, up or down, due to the
non-uniform magnetic field
Classically, we expect a continuous pattern of silver deposited on the glass
Experimentally, we observe a quantized pattern of silver deposited on the glass
Demo of Quantum Mechanics

8. Electric Motors B B 10 8

9. Electric Generators
Tangential speed:
Force on charges: 10 9

10. Electric Generators
AC generator 10 10

11. Power Required to Turn a Generator10 11

12. A Clicker Question (similar to last lec.)B) C) D)

13. Q1) A) B) C) D) Both cases are in equilibrium,
but only the top one is stable.

14. Patterns of Fields in Space
Chapter 22
Patterns of Fields in Space
Electric flux
Gauss’s law
Ampere’s law
Maxwell equations 14

16. Clicker Q2 A) B) C) D) E)

17. Clicker Q2 A) B) C) D) E) B

20. Proving Gauss’s Law
E-field superposition