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

law change field Current force direct examples

Force Law 1 B → qv → F = qv x B RHR 1 charge deflection picture tube

Force Law 2 B → il → F = il x B RHR 1 2 wires, motor, loudspeaker

Ampere’s Law

B = μoi/2πr ← i RHR 2 electromagnet solenoid

Faraday Induction

d/dt → Φ = B*A → ε = dΦ/dt i = ε/R

Lentz generator 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• Ampere’s Law

• Symmetric loop around current I

• Units– μo = 4π x 10-7 T-m/A “permeability of free space”

– Electric forms “spokes” magnetic forms “loops”– Electromagnetic field

Right hand rule II

• Right hand rule for current carrying wire

Example 20-7

• Ampere’s Law for long wire

• Direction: down into the page at point P

Example 20-8

• For B1

• For B2

• Total field (by inspection)

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

• Wire 1 sets up field.

• Wire 2 feels force of that field.

• And vice versa (wire 2 on 1)

• F21=-F12 by action-reaction

Force between parallel wires - 2

a) currents same directionb) currents opposite direction

action-reaction pair

Magnetism and Induction Flowchart

law change field Current force direct examples

Force Law 1 B → qv → F = qv x B RHR 1 charge deflection picture tube

Force Law 2 B → il → F = il x B RHR 1 2 wires, motor, loudspeaker

Ampere’s Law

B = μoi/2πr ← i RHR 2 electromagnet solenoid

Faraday Induction

d/dt → Φ = B*A → ε = dΦ/dt i = ε/R

Lentz generator transformer

Wire 1 creates magnetic fieldWire 2 feels force of that field

Example 20-10

• Field of first wire

• Force felt on second wire

Example 20-11

• Field of first wire

• Force on second wire

Problem 41•

Problem 43•

Problem 45

•

Rotating current loop• Force on each side of loop (fig a/b)

– Left – Right

• Moment arm of each torque (fig c)

• Torque of both sides

• For N loops of wire

φ

DC motor

• Current reverses every half turn • DC motor

DC Motor animation• DC motor animation

• http://educypedia.karadimov.info/library/MccComplet.swf

D.C. Motor.swf

MccComplet.swf

Loudspeaker

•