Magnetic Fields Gauss’s Law vs. Ampere’s Law Ampere’s Law Ampere’s Law for long straight wire Examples Magnetic properties of materials Force between 2 parallel wires Motors Loudspeakers

Magnetism and Induction Flowchart lawchangefieldCurrentforcedirectexamples Force Law 1B →qv →F = qv x BRHR 1charge deflection picture tube Force Law 2B →il →F = il x BRHR 12 wires, motor, loudspeaker Ampere’s Law B = μ o i/2πr← iRHR 2electromagnet solenoid Faraday Induction d/dt →Φ = B*A →ε = dΦ/dt i = ε/R Lentzgenerator transformer Current creates magnetic field

Gauss’s vs. Ampere’s Law Gauss’s Law for closed surface – Flux lines penetrating closed surface equals charge enclosed. Ampere’s Law for closed loop – Magnetic field integrated along closed loop equals current enclosed.

Ampere’s Law for long straight wire

Right hand rule II Right hand rule for current carrying wire

Example 20-7

Example 20-8

Example 20-9

Magnetism in materials Spinning charge particle creates magnetic field If all spinning particles align, you have a magnet

Force between parallel wires - 1

Force between parallel wires - 2 a)currents same direction b)currents opposite direction action-reaction pair

Magnetism and Induction Flowchart lawchangefieldCurrentforcedirectexamples Force Law 1B →qv →F = qv x BRHR 1charge deflection picture tube Force Law 2B →il →F = il x BRHR 12 wires, motor, loudspeaker Ampere’s Law B = μ o i/2πr← iRHR 2electromagnet solenoid Faraday Induction d/dt →Φ = B*A →ε = dΦ/dt i = ε/R Lentzgenerator transformer Wire 1 creates magnetic field Wire 2 feels force of that field

Example 20-10

Example 20-11

Problem 41

Problem 43

Problem 45

Rotating current loop φ

DC motor Current reverses every half turn DC motor

DC Motor animation DC motor animation

Loudspeaker