Magnetic fields in matter Week 13 Magnetic fields in matter

I(out) B I(in) The force on a segment of wire L is MD12-7 The force on a segment of wire L is A current-carrying wire loop is in a constant magnetic field B = B z_hat as shown. What is the direction of the torque on the loop? A) Zero B) +x C) +y D) +z E) None of these z B y z I(in) I(out) B y I x

Griffiths argues that the torque on a magnetic dipole in a B field is: 6.1 Griffiths argues that the torque on a magnetic dipole in a B field is: How will a small current loop line up if the B field points uniformly up the page? CORRECT ANSWER: B USED IN: Spring 2008 (Pollock) LECTURE NUMBER: 37 STUDENT RESPONSES: 0% [[87%]] 0% 13% 0% INSTRUCTOR NOTES: 87% correct. 2 voted for D. I pointed out to them to think about it in two ways - by the torque formula, but also thinking about I L cross B for pieces of a tilted loop. (And, we discussed the "metastability" of answer A, which several students raised) -SJP WRITTEN BY: Steven Pollock (CU-Boulder)

Griffiths argues that the force on a magnetic dipole in a B field is: 6.2 Griffiths argues that the force on a magnetic dipole in a B field is: If the dipole m points in the z direction, what can you say about B if I tell you the force is in the x direction? m F x y z B simply points in the x direction B) Bz must depend on x C) Bz must depend on z D) Bx must depend on x E) Bx must depend on z CORRECT ANSWER: B USED IN: Spring 2008 (Pollock) LECTURE NUMBER: 37 STUDENT RESPONSES: 7% [[67%]] 13% 7% 7% INSTRUCTOR NOTES: Only 2/3 got this one right! Lot of confusion on many of their parts about how to think about this conceptuallly? Note that it's basically identical to an earlier question we had about electric dipoles. Answer: B. m dot B will be m Bz, so if the force has only an x component, then Bz must depend (only!) on X. -SJP WRITTEN BY: Steven Pollock (CU-Boulder)

Everywhere: throughout the volume and on all surfaces 6.3 A solid cylinder has uniform magnetization M throughout the volume in the z direction as shown. Where do bound currents show up? Everywhere: throughout the volume and on all surfaces Volume only, not surface Top/bottom surface only Side (rounded) surface only All surfaces, but not volume CORRECT ANSWER: D USED IN: Spring 2008 (Pollock) LECTURE NUMBER:39 STUDENT RESPONSES: 0% 12% 0% [[ 88%]] 0% INSTRUCTOR NOTES: 88% correct. Too easy. No problems, 2 people voted for B (with no explanation) My answer: D. (Mxn is nonzero there). -SJP WRITTEN BY: Steven Pollock (CU-Boulder)

Something else, it's more complicated 6.4 A solid cylinder has uniform magnetization M throughout the volume in the x direction as shown. What's the magnitude of the total magnetic dipole moment of the cylinder? R2 L M 2R L M 2R M R 2M Something else, it's more complicated CORRECT ANSWER: A USED IN: Spring 2008 (Pollock) LECTURE NUMBER: 39 STUDENT RESPONSES: [[100%]] 0% 0% 0% 0% INSTRUCTOR NOTES: Started with this. 100% correct. Little too easy, eh? -SJP WRITTEN BY: Steven Pollock (CU-Boulder)

Top/bottom surface only Side (rounded) surface only Everywhere 6.5 A solid cylinder has uniform magnetization M throughout the volume in the x direction as shown. Where do bound currents show up? Top/bottom surface only Side (rounded) surface only Everywhere Top/bottom, and parts of (but not all of) side surface (but not in the volume) Something different/other combination! CORRECT ANSWER: D USED IN: Spring 2008 (Pollock) LECTURE NUMBER: 39 STUDENT RESPONSES: 0% 0% 6% [[94%]] 0% INSTRUCTOR NOTES: 94% , all but 1. Too easy once again today, they're having no problem with any of these. Answer D. (right and left edges have no current, it "wraps around" the top front bottom and back. -SJP WRITTEN BY: Steven Pollock (CU-Boulder)

To discuss: A solid cylinder has uniform magnetization M throughout the volume in the z direction as shown. What will the B field look like? (Consider if the cylinder is tall and thin, or short and fat, separately) CORRECT ANSWER: n/a USED IN: Spring 2008 (Pollock) LECTURE NUMBER: 39 STUDENT RESPONSES: n/a INSTRUCTOR NOTES: We discussed this briefly, they seemed to have it... -SJP WRITTEN BY: Steven Pollock (CU-Boulder)

Which way is the bound current flowing? +z everywhere B) +x everywhere MD13-1 In the interior of a magnet, the magnetization increases from left to right like so: x y Z(out) x z y(out) Which way is the bound current flowing? +z everywhere B) +x everywhere C) +z and –z D) +x and –x E) other!

A sphere has uniform magnetization M in the z direction. 6.6 A sphere has uniform magnetization M in the z direction. Which formula is correct for this surface current? A) B) C) D) E) None of these! CORRECT ANSWER: B USED IN: Spring 2008 (Pollock) LECTURE NUMBER: 39 STUDENT RESPONSES: 18% [[76%]] 6% 0% 0% INSTRUCTOR NOTES: 76% B, with all others (except 1) voting A. Some discussion of Griffiths' notation, this was another in a chain of easy ones today. Not sure why 4 people voted wrong. This one was a segue into the discussion of what the *formula* for the resulting B field is (since we solved the revolving charged sphere problem last week, and derived the B field in and out for that). Surface current is M cross Rhat, so if M is in the z direction, then you get Answer B. -SJP WRITTEN BY: Steven Pollock (CU-Boulder)