W07D1 Magnetic Dipoles, Force and Torque on a Dipole, Experiment 2 W07D1 Magnetic Dipoles, Torque and Force on a Dipole, Experiment 2: Magnetic Dipole in a Helmholtz Coil http://web.mit.edu/8.02t/www/materials/Experiments/expMagForcesDipoleHelmholtz.pdf Reading Course Notes: Sections 8.4, 8.6.4, 8.10.4, 8.13, 9.5, 9.9 Class 18

Announcements Exam Two Reviews: Monday from 7-9 pm in 26-152 Tuesday from 9-11 pm in 26-152 Wednesday from 9-11 pm in 26-152 PS 6 due W07 Tuesday at 9 pm in boxes outside 32-082 or 26-152 Exam 2 Thursday March 21 7:30 - 9:30 pm: See announcement pages for section room assignments Conflict Friday March 22 9-11 am in 32-082; 10-12 noon in 6-120 Class 15

Magnetic Field of Bar Magnet (1) A magnet has two poles, North (N) and South (S) (2) Magnetic field lines leave from N, end at S Class 12

Magnetism – Bar Magnet Like poles repel, opposite poles attract Class 12

Bar Magnets Are Dipoles! Create Dipole Field Rotate to orient with Field Is there magnetic “mass” or magnetic “charge?” NO! Magnetic monopoles do not exist in isolation Class 12

Magnetic Monopoles? Electric Dipole Magnetic Dipole -q q When cut: 2 monopoles (charges) When cut: 2 dipoles Magnetic monopoles do not exist in isolation Another Maxwell’s Equation! (2 of 4) Gauss’s Law Magnetic Gauss’s Law Class 12

Conservation of Magnetic Flux: Class 12

Torque on a Current Loop in a Uniform Magnetic Field Class 18

Review: Magnetic Force on Current-Carrying Wire If the wire is a uniform magnetic field then If the wire is also straight then Class 18

Group Problem: Current Loop Place rectangular current loop in uniform B field 1) What is the net force on this loop? 2) What is the net torque on this loop? 3) Describe the motion the loop makes Class 18

Torque on Rectangular Loop Area vector x No net force but there is a torque Class 18

Magnetic Dipole Moment http://web.mit.edu/viz/EM/visualizations/magnetostatics/calculatingMagneticFields/RingMagField/RingMagField.htm Class 15

Torque on Current Loop Place rectangular current loop in uniform B field Magnetic moment points out of the page torque tries to align the magnetic moment vector in the direction of the magnetic field Class 18

Concept Question: Magnetic Field Lines The picture shows the field lines outside a permanent magnet The field lines inside the magnet point: Up Down Left to right Right to left The field inside is zero I don’t know Class 15

Concept Q. Answer: Magnetic Field Lines Answer: 1. They point up inside the magnet Magnetic field lines are continuous. E field lines begin and end on charges. There are no magnetic charges (monopoles) so B field lines never begin or end Class 15

Demonstration: Deflection of a Compass Needle by a Magnet G1 http://tsgphysics.mit.edu/front/?page=demo.php&letnum=G%201&show=0 Class 12

Demonstration: Galvanometer principle G10 http://tsgphysics.mit.edu/front/?page=demo.php&letnum=G%2010&show=0 Class 18

Concept Question: Dipole in Field m From rest, the coil above will: rotate clockwise, not move rotate counterclockwise, not move move to the right, not rotate move to the left, not rotate move in another direction, without rotating both move and rotate neither rotate nor move I don’t know Class 18

Concept Q. Answer: Dipole in Field Answer: 1. Coil will rotate clockwise (not move) No net force so no center of mass motion. BUT Magnetic dipoles rotate to align with external field (think compass) Class 18

Force on a Dipole in a Non-Uniform Field Class 18

Dipoles don’t move??? This dipole rotates but doesn’t feel a net force in a uniform magnetic field But dipoles can feel magnetic force. Class 18

Dipoles in Non-Uniform Fields: Magnetic Force Class 18

Concept Question: Dipole in Field The current carrying coil above will feel a net force upwards downwards of zero I don’t know Class 18

Concept Q. Answer: Dipole in Field Answer: 2. Feels downward force. The forces shown produce a net downward force Class 18

Force on Magnetic Dipole S m N S What makes the field pictured? Bar magnet below dipole, with N pole on top. It is aligned with the dipole pictured, they attract! Class 18

Work Done by Interaction to Anti-align Magnetic Dipole \begin{vmatrix}\vec{\tau}\end{vmatrix} = \mu B \sin \theta W = -\int_0^\pi \tau d\theta = -\int_0^\pi \mu B \sin \theta \,d\theta Class 15

Potential Energy: Dipole in Magnetic Field Set zero reference point Lowest energy state (aligned) : Highest energy state (anti-aligned):

Force on Magnetic Dipole S N S along z-axis Class 18

Magnetic Field Profiles Experiment 2 Week 08, Day 2 Week 08, Day 2Week 08, Day 2 Magnetic Field Profiles Experiment 2 Class 19 Class 19Class 19 29

Concept Question: Dipole in Helmholtz Week 08, Day 2 Week 08, Day 2Week 08, Day 2 Concept Question: Dipole in Helmholtz A dipole pointing along the positive x-direction and located at the center of a Helmholtz coil will feel: a force but not a torque. a torque but not a force. both a torque and a force. neither force nor torque. Class 19 Class 19Class 19 30

Concept Q. Answer: Dipole in Helmholtz Week 08, Day 2 Week 08, Day 2Week 08, Day 2 Concept Q. Answer: Dipole in Helmholtz Answer: 2. a torque but not a force. The Helmholtz coil makes a UNIFORM FIELD. Dipole feels only torque (need gradient for force). Class 19 Class 19Class 19 31

Concept Question: Dipole in Anti-Helmholtz Coil Week 08, Day 2 Week 08, Day 2Week 08, Day 2 Concept Question: Dipole in Anti-Helmholtz Coil A dipole pointing along the positive z-direction and located at the center of an anti- Helmholtz coil will feel: a force but not a torque. a torque but not a force. both a torque and a force. neither force nor torque. Class 19 Class 19Class 19 32

Concept Q. Answer: Dipole in Anti-Helmholtz Coil Week 08, Day 2 Week 08, Day 2Week 08, Day 2 Concept Q. Answer: Dipole in Anti-Helmholtz Coil Answer: 1. A force because there is a gradient in the magnetic field but no torque because the magnetic field at the center is zero. Class 19 Class 19Class 19 33

Experiment 2: Magnetic Forces on Dipole in Fields of Helmholtz Coil Week 08, Day 2 Week 08, Day 2Week 08, Day 2 Experiment 2: Magnetic Forces on Dipole in Fields of Helmholtz Coil Class 19 Class 19Class 19 34

Getting Started: Set up current supply Week 08, Day 2 Week 08, Day 2Week 08, Day 2 Getting Started: Set up current supply Open circuit (disconnect a lead) Turn current knob full CCW (off) Increase voltage to ~12 V This will act as a protection: V<12 V Reconnect leads in Helmholtz mode Increase current to ~1 A Class 19 Class 19Class 19 35

Week 08, Day 2 Week 08, Day 2Week 08, Day 2 Appendix Experiment 2: Magnetic Forces on Dipole in Fields of Helmholtz Coil Field Configurations and Concept Questions Class 19 Class 19Class 19 36

Appendix 2: Gauss’s Law for Magnetism Week 08, Day 2 Week 08, Day 2Week 08, Day 2 Appendix 2: Gauss’s Law for Magnetism Class 19 Class 19Class 19 37

Animation: Magnetic Field Generated by a Current Loop http://web.mit.edu/viz/EM/visualizations/magnetostatics/calculatingMagneticFields/RingMagInt/RingMagIntegration.htm Class 18

Demonstration: Magnetic Field Lines from Bar Magnet G2 http://tsgphysics.mit.edu/front/?page=demo.php&letnum=G%202&show=0 Class 12