1 Chapter 21 Magnet Forces and Magnetic Fields

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1 Chapter 21 Magnet Forces and Magnetic Fields

1 Chapter 21 Magnet Forces and Magnetic Fields

2 1) Magnets and Magnetic Fields a) Natural permanent magnets – Like poles repel,

2 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

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

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

4 c) Field of dipole

4 c) Field of dipole

5 d) Magnetostatics for poles (identical to electrostatics for charges) – 2 types: N,

5 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:

6 e) Why study magnetism? – No monopoles (yet) – Poles (dipoles) produced by

6 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

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

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

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8

9 3) Magnetic force on current a) Orthogonal case Force per unit length defines

9 3) Magnetic force on current a) Orthogonal case Force per unit length defines B Direction from RHR 1: B fingers, I thumb, F palm

10 Units:

10 Units:

11 b) General case Force per unit length

11 b) General case Force per unit length

12 4) Force between parallel wires

12 4) Force between parallel wires

13 FE + FB FB + v v FE Attraction or repulsion? Does it

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

15 • Define Ampere as the quantity of current that produces a force per

15 • 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 • Then • This defines C and gives

16 • Permeability of free space Then

16 • Permeability of free space Then

17 5) Field due to long straight wire (magnitude)

17 5) Field due to long straight wire (magnitude)

18 6) Force on a moving charge • Zero at rest • Zero parallel

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

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

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

20 7) Motion of a charge in a magnetic field a) Constant force motion

20 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

21 b) Constant magnitude perpendicular to motion radial field (circular motion) mass on a

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

Force due to the field: 22 For circular motion: So, r depends on v,

Force due to the field: 22 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

Tracks in a bubble chamber • electron-positron creation • 1, 3 positive • 2 negative • energy: 3 > 2 > 1 • energy decreases by collisions 23

24 Example: Find speed and radius for proton B = 0. 10 T V

24 Example: Find speed and radius for proton B = 0. 10 T V = 2100 V

25 c) Work done by magnetic field Work by a force F F displacement,

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

26 d) Velocity selector Force due to E (down): Force due to B (up):

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

27 e) Mass Spectrometer Ion energy: Radius of motion:

27 e) Mass Spectrometer Ion energy: Radius of motion: