As You Come In… Write down 3 things you already know about magnetism.

Field Behaviors Charged particles behave certain ways when placed in certain fields For stationary particle: Gravitational field: moves toward a mass electron g FgFg

Field Behaviors Charged particles behave certain ways when placed in certain fields For stationary particle: Gravitational field: moves toward a mass Electrical field: moves toward an opposite charge or away from like charge electron E FEFE

S Field Behaviors Charged particles behave certain ways when placed in certain fields For stationary particle: Gravitational field: moves toward a mass Electrical field: moves toward an opposite charge or away from like charge Magnetic field: doesn’t move at all electron B N

Field Behaviors electron g FgFg Now take the case of a moving particle For moving particle: Gravitational field: still moves toward a mass v

Field Behaviors g Now take the case of a moving particle For moving particle: Gravitational field: still moves toward a mass

Field Behaviors g Now take the case of a moving particle For moving particle: Gravitational field: still moves toward a mass

Field Behaviors g Now take the case of a moving particle For moving particle: Gravitational field: still moves toward a mass

Field Behaviors g Now take the case of a moving particle For moving particle: Gravitational field: still moves toward a mass

Field Behaviors g Now take the case of a moving particle For moving particle: Gravitational field: still moves toward a mass

Field Behaviors g Now take the case of a moving particle For moving particle: Gravitational field: still moves toward a mass

Field Behaviors g Now take the case of a moving particle For moving particle: Gravitational field: still moves toward a mass

Field Behaviors g Now take the case of a moving particle For moving particle: Gravitational field: still moves toward a mass

Field Behaviors g Now take the case of a moving particle For moving particle: Gravitational field: still moves toward a mass

Field Behaviors E Now take the case of a moving particle For moving particle: Gravitational field: still moves toward a mass Electrical field: still moves toward an opposite charge or away from like charge electron FEFE v

Field Behaviors E Now take the case of a moving particle For moving particle: Gravitational field: still moves toward a mass Electrical field: still moves toward an opposite charge or away from like charge

Field Behaviors E Now take the case of a moving particle For moving particle: Gravitational field: still moves toward a mass Electrical field: still moves toward an opposite charge or away from like charge

Field Behaviors E Now take the case of a moving particle For moving particle: Gravitational field: still moves toward a mass Electrical field: still moves toward an opposite charge or away from like charge

Field Behaviors E Now take the case of a moving particle For moving particle: Gravitational field: still moves toward a mass Electrical field: still moves toward an opposite charge or away from like charge

Field Behaviors E Now take the case of a moving particle For moving particle: Gravitational field: still moves toward a mass Electrical field: still moves toward an opposite charge or away from like charge

Field Behaviors E Now take the case of a moving particle For moving particle: Gravitational field: still moves toward a mass Electrical field: still moves toward an opposite charge or away from like charge

Field Behaviors E Now take the case of a moving particle For moving particle: Gravitational field: still moves toward a mass Electrical field: still moves toward an opposite charge or away from like charge

Field Behaviors E Now take the case of a moving particle For moving particle: Gravitational field: still moves toward a mass Electrical field: still moves toward an opposite charge or away from like charge

Field Behaviors E Now take the case of a moving particle For moving particle: Gravitational field: still moves toward a mass Electrical field: still moves toward an opposite charge or away from like charge

Field Behaviors Now take the case of a moving particle For moving particle: Gravitational field: still moves toward a mass Electrical field: still moves toward an opposite charge or away from like charge S B N electron v

Field Behaviors Now take the case of a moving particle For moving particle: Gravitational field: still moves toward a mass Electrical field: still moves toward an opposite charge or away from like charge S B N

Field Behaviors Now take the case of a moving particle For moving particle: Gravitational field: still moves toward a mass Electrical field: still moves toward an opposite charge or away from like charge S B N

Field Behaviors Now take the case of a moving particle For moving particle: Gravitational field: still moves toward a mass Electrical field: still moves toward an opposite charge or away from like charge S B N

Field Behaviors Now take the case of a moving particle For moving particle: Gravitational field: still moves toward a mass Electrical field: still moves toward an opposite charge or away from like charge S B N

Field Behaviors Now take the case of a moving particle For moving particle: Gravitational field: still moves toward a mass Electrical field: still moves toward an opposite charge or away from like charge S B N

Field Behaviors Now take the case of a moving particle For moving particle: Gravitational field: still moves toward a mass Electrical field: still moves toward an opposite charge or away from like charge S B N

Field Behaviors Now take the case of a moving particle For moving particle: Gravitational field: still moves toward a mass Electrical field: still moves toward an opposite charge or away from like charge S B N

Field Behaviors Now take the case of a moving particle For moving particle: Gravitational field: still moves toward a mass Electrical field: still moves toward an opposite charge or away from like charge S B N

Field Behaviors Now take the case of a moving particle For moving particle: Gravitational field: still moves toward a mass Electrical field: still moves toward an opposite charge or away from like charge S B N

Field Behaviors Now take the case of a moving particle For moving particle: Gravitational field: still moves toward a mass Electrical field: still moves toward an opposite charge or away from like charge S B N

Field Behaviors Now take the case of a moving particle For moving particle: Gravitational field: still moves toward a mass Electrical field: still moves toward an opposite charge or away from like charge S B N

Field Behaviors Now take the case of a moving particle For moving particle: Gravitational field: still moves toward a mass Electrical field: still moves toward an opposite charge or away from like charge S B N

Field Behaviors Now take the case of a moving particle For moving particle: Gravitational field: still moves toward a mass Electrical field: still moves toward an opposite charge or away from like charge S B N

Field Behaviors Now take the case of a moving particle For moving particle: Gravitational field: still moves toward a mass Electrical field: still moves toward an opposite charge or away from like charge S B N

Field Behaviors Now take the case of a moving particle For moving particle: Gravitational field: still moves toward a mass Electrical field: still moves toward an opposite charge or away from like charge S B N

Field Behaviors Now take the case of a moving particle For moving particle: Gravitational field: still moves toward a mass Electrical field: still moves toward an opposite charge or away from like charge S B N

Field Behaviors Now take the case of a moving particle For moving particle: Gravitational field: still moves toward a mass Electrical field: still moves toward an opposite charge or away from like charge S B N

Field Behaviors Now take the case of a moving particle For moving particle: Gravitational field: still moves toward a mass Electrical field: still moves toward an opposite charge or away from like charge S B N

Field Behaviors Now take the case of a moving particle For moving particle: Gravitational field: still moves toward a mass Electrical field: still moves toward an opposite charge or away from like charge S B N

Field Behaviors Now take the case of a moving particle For moving particle: Gravitational field: still moves toward a mass Electrical field: still moves toward an opposite charge or away from like charge Magnetic field: moves outward?????? S B N

S Field Behaviors Now take the case of a moving particle For moving particle: Gravitational field: still moves toward a mass Electrical field: still moves toward an opposite charge or away from like charge Magnetic field: moves outward?????? B FBFB N electron v

S Force Equations Gravitational force: F g = mg Electrical force: F E = qE Magnetic force (Lorentz force): F B = qv × B B FBFB N electron v

S Cross Product Recap Recall that v 1 × v 2 is a cross product Product is a vector—has magnitude and direction Finding magnitude: ǁv 1 × v 2 ǁ = v 1 v 2 sin(δ) If δ = 90°, simplifies to ǁv 1 × v 2 ǁ = v 1 v 2 Finding direction: Right-hand Rule B FBFB N electron v

S Finding Magnetic Force Magnetic force: F B = qv × B Magnitude of F B ǁqv × Bǁ = qvBsin(δ) If δ = 90°, simplifies to ǁqv × Bǁ = qvB Direction of F B Right-hand Rule B FBFB N electron v

Finding Magnetic Force Magnetic force: F B = qv × B Magnitude of F B ǁqv × Bǁ = qvBsin(δ) If δ = 90°, simplifies to ǁqv × Bǁ = qvB Direction of F B Right-hand Rule Fingers are magnetic field lines Thumb is velocity of particle Force is palm of hand Fingers: B Thumb: v Palm: F (facing inward) Wait a sec…wasn’t the force directed outward before???

Charge and Sign Conventions Charge of particle affects direction of force Positive charge: force points according to right-hand rule Negative charge: force points in opposite direction of right-hand rule Alternative: Positive charges: right-hand rule Negative charges: left-hand rule Fingers: B Thumb: v Palm: F (facing inward)

About Magnetic Fields Nikola Tesla Image obtained from:

About Magnetic Fields Cool magnetic field intensities to know: 0.5 pT: average B of human brain 45 µT: average B of Earth’s magnetosphere 5 mT: average B of refrigerator magnet 1.25 T: B of strongest rare-earth magnet 2 T: average B of medical MRI machinesMRI machines 16 T: B used to levitate 25 g frog 45 T: strongest continuous B field ever produced Carl Friedrich Gauss Image obtained from:

Tweaking the Lorentz Force l B I

Currents & Magnetic Force Magnetic force on a current-carrying wire: F B = l I × B Magnitude of F B ǁ l I × Bǁ = l I Bsin(δ) If δ = 90°, simplifies to ǁ l I × Bǁ = l I B Direction of F B Right-hand Rule Fingers are magnetic field lines Thumb is direction of current Force is palm of hand l I B FBFB