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

Lowest energy   = 0

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

Force on a magnetic dipole 1 2 Magnitude: Need B-field distribution Direction: Attractive

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

Bar magnet is equivalent to a magnetic dipole Silver atoms

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

Electric Motors B B 10 8

Electric Generators Tangential speed: Force on charges: 10 9

Electric Generators AC generator 10 10

Power Required to Turn a Generator 10 11

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

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

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

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

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

Proving Gauss’s Law E-field superposition