Exploring Magnet Forces and Magnetic Fields in Chapter 21

Chapter 21 Magnet Forces and Magnetic Fields

1) Magnets and Magnetic Fields a) Natural permanent magnets • Like poles repel, unlike attract • come in pairs (no monopoles) • Interact with earth; define N (or north-seeking) pole as pole attracted to North pole of earth

b) Magnetic field direction: - direction of force on N pole B

c) Field of dipole

d) Magnetostatics for poles (identical to electrostatics for charges) • 2 types: N, S vs +,- • Unlike attract, like repel • Inverse square law • Force along joining line • Magnetic Field:

e) Why study magnetism? • No monopoles (yet) • Poles (dipoles) produced by moving charges (no direct control of pole distribution) • Charges affected by magnetic field i.e. fundamental unit is still charge; want magnetic field due to charge, and force on charge due to magnetic field

2) Magnetic field due to current(direction) • Oersted (1820)

Forceper unit length 3) Magnetic force on current a) Orthogonal case Direction from RHR1: B fingers, I thumb, F palm defines B

Units:

Force per unit length b) General case

4) Force between parallel wires

FE v FB FB v FE + + Attraction or repulsion? Does it depend on reference frame?

- - - - - - + + + + + + v v

• Then • Define Ampere as the quantity of current that produces a force per unit length of 2 x 10-7 N/m for separation of 1 m • This defines C and gives

Then • Permeability of free space

5) Field due to long straight wire(magnitude)

6) Force on a moving charge • Zero at rest • Zero parallel to B • Max perpendicular to B

• Proportional to component of v perp to B (Alternative definition of B) • Perpendicular to B • Perpendicular to v

7) Motion of a charge in a magnetic field a) Constant force motion is parabolic electric or gravitational field not everywhere perp to velocity not magnetic field

radial field (circular motion) mass on a string b) Constant magnitude perpendicular to motion motion is circular magnetic field produces circular motion (initial vel. perp. to B)

Force due to the field: For circular motion: So, r depends on v, B angular freq. independent of speed, radius

Tracks in a bubble chamber • electron-positron creation • 1, 3 positive • 2 negative • energy: 3 > 2 > 1 • energy decreases by collisions

Example: Find speed and radius for proton B = 0.10 T V = 2100 V

F displacement, x Work by a force F c) Work done by magnetic field For a magnetic field, Work = 0

Force due to E (down): d) Velocity selector Force due to B (up): For zero deflection, FE = FB :

Ion energy: e) Mass Spectrometer Radius of motion:

Exploring Magnet Forces and Magnetic Fields in Chapter 21

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