Lecture 21—Wednesday

March 18Magnetic Forces on Dipoles

Magnetic Resonance Imaging

Quick Review of Monday

• Force on a straight wire in a uniform B-field:

– Direction from right hand rule• Force between two straight parallel

conductors:

– Direction from right hand rule

sinWIREF ILB

Fparallel wires 0LI1I2

2d

Today

• Force on a magnetic dipole in a magnetic field– Current loop is a magnetic dipole

• Find torque on a planar current loop– Start with rectangular loop

• Magnetic Resonance Imaging– Atoms are dipoles

• But only two orientations wrt magnetic field, with or against. Difference in energy between the two orientations is in the radio frequency range for B≈1 T

Bar magnet in uniform B-field

a b c d

25% 25%25%25%

c

d

1. a2. b3. c4. d

Magnetic Fields Exert Torques on Current Loops

Slide 24-42

The Torque on a Dipole in a Magnetic Field

IA B sin

Slide 24-43

The Electric Motor

Slide 24-46

Magnetic Resonance Imaging

Slide 24-44

Magnetic Resonance Imaging

Slide 24-45

Quiz #8

• What magnetic field strength and direction will levitate the 2.0g wire? B-field in shaded region.

1.5A

Homework due today

• Homework due today– Problems: 24: 32, 34, 37

• 32: field strength and direction to levitate wire given mass and I

• 34: F with wire not perpendicular to field• 37: force on current loop with radial field (loud

speaker).

Homework due Friday

• Read: 23: 1-3 Faraday’s Law and electromagnetic induction

• Problems: 24: 38, 39, WB 24:23-30• 38: torque on current loop• 39: ditto• WB 24: 23-30 forces on straight wires and torques on

loops