Your Comments You know, I really wish the homework was do-able without arcane mastery of geometry... i don't understand how to use magnetic dipole moment at all

Those eyes in the prelecture look so sad, even though the physics is so exciting.

Can you PLEASE go over RC Circuits again because it doesn't really make sense to me

How do we chose a direction on the vector length L? Is it arbitrary?

I did not understand the dipole moment and potential energy part. Also can you please clarify how to find direction of things using various right hand rules. I'm getting confused!

Today (26 Feb) is my birthday, so I wanted to send out a message to celebrate my 19th. Torque was hard in 211...I don't even want to think about it in 212 :( Is the area (A) in the equation (for dipole moment and torque) actually the cross sectional area? So is it just the amount of area that the magnetic field passes through? Or is it the total area enclosed by the loop?

You know, I don't say this often, but this magnetism stuff is kind of interesting. Almost makes me wish I wasn't a bioengineer and I was an ECE major. Almost.

Electricity & Magnetism Lecture 13, Slide 1 Physics 212 Lecture 13

Today’s Concept: Torques

Electricity & Magnetism Lecture 13, Slide 2 Last Time: F qv B

This Time:    z F  q v  B y  i F i B

      I x F  qNvavg  B F  IL B N  nAL

I  qnAvavg

Electricity & Magnetism Lecture 13, Slide 3 Clicker Question

   F  IL B

A A. B B. C C.

Electricity & Magnetism Lecture 13, Slide 4 Clicker Question

   F  IL B

A A. B B. C C.

Electricity & Magnetism Lecture 13, Slide 5 Clicker Question

   F  IL B

What is the force on section d-a of the loop? A) Zero B) Out of the page C) Into the page

Electricity & Magnetism Lecture 13, Slide 6 CheckPoint 1a

A square loop of wire is carrying current in the counterclockwise direction. There is a horizontal uniform magnetic field pointing to the right.

What is the direction on the net force on the loop? A. Out of the page B. Into of the page C. The net force on the loop is zero “it is a closed loop (length vector is 0) so the net force is 0 F = ILxB = 0

Electricity & Magnetism Lecture 13, Slide 7 CheckPoint 1b

y

x

In which direction will the loop rotate? (assume the z axis is out of the page)

A) Around the x axis B) Around the y axis C) Around the z axis D) It will not rotate

Electricity & Magnetism Lecture 13, Slide 8 CheckPoint 1c

  F  R   R F

What is the direction of the net torque on the loop?

A. Up B. Down C. Out of the page D. Into the page E. The net torque is zero

r x f = torque Electricity & Magnetism Lecture 13, Slide 9 Magnetic Dipole Moment

EXPLAIN THE MAGNETIC DIPOLE... What IS IT?!?!?!?!!?!?!

Area vector Magnitude = Area Direction uses R.H.R.

Magnetic Dipole moment     NIA

Electricity & Magnetism Lecture 13, Slide 10  Makes Torque Easy!        B The torque always wants to line  up with B!

z turns  toward B

z  y B x  y B x turns  toward B

Electricity & Magnetism Lecture 13, Slide 11 Practice with  and         B I B 

In this case  is out of the page (using right hand rule)

z        B is up (turns  toward B)

 y x B

Electricity & Magnetism Lecture 13, Slide 12 CheckPoint 2a

Three different orientations of a magnetic dipole moment in a constant magnetic field are shown below. Which orientation results in the largest magnetic torque on the dipole?

       B   Biggest when   B

Electricity & Magnetism Lecture 13, Slide 13 Magnetic Field can do Work on Current

From Physics 211: W  d From Physics 212:   BB  sin(  ) W  Bsin(  ) d    B cos(  )    B

1.5

1 U  W 0.5

0 Define U  0 at position of 0 30 60 90 120 150 180 maximum torque -0.5    -1 U    B -1.5 B

Electricity & Magnetism Lecture 13, Slide 14 CheckPoint 2b

f  U  Bcos U  +Bcosf U  0

  U    B

Electricity & Magnetism Lecture 13, Slide 15 ACT

Three different orientations of a magnetic dipole moment in a constant magnetic field are shown below. We want to rotate the dipole in the CCW direction.

a

fa c B

First, consider rotating to position c. What are the signs of the work done by you and the work done by the field? WU  A) Wyou > 0, Wfield > 0 field B) Wyou > 0, Wfield < 0 • U > 0, so Wfield < 0. Wyou must be opposite Wfield C) Wyou < 0, Wfield > 0 • Also, torque and displacement in opposite directions  D) Wyou < 0, Wfield < 0 Wfield < 0

30 Physics 212 Lecture 13, Slide 16 CheckPoint 2c Three different orientations of a magnetic dipole moment in a constant magnetic field are shown below. In order to rotate a horizontal magnetic dipole to the three positions shown, which one requires the most work done by the magnetic field?

a

fa c

BY BY YOU FIELD

W  U U U by_ field   i f U    B

C): Wby_ field  B (Bcosc )  B(1cosc )

B): Wby_ field  B 0  B

A): Wby_ field  B (Bcosa )  B(1+ cosfa )

Electricity & Magnetism Lecture 13, Slide 17 Calculation z z A square loop of side a lies in the xz plane with B B current I as shown. The loop can rotate about x 30˚. axis without friction. A uniform field B points along the +z axis. Assume a, I, and B are known. y y a How much does the potential energy of the I system change as the coil moves from its x final initial initial position to its final position. Conceptual Analysis A current loop may experience a torque in a constant magnetic field    X B We can associate a potential energy with the orientation of loop U    ∙ B

Strategic Analysis Find  Calculate the change in potential energy from initial to final

Electricity & Magnetism Lecture 13, Slide 18 Calculation z z A square loop of side a lies in the xz plane with B B current I as shown. The loop can rotate about x 30˚. axis without friction. A uniform field B points   along theLA +z axis. Assume a, I, and B are known. y y a I x finalfinal initialinitial

What is the direction of the magnetic moment of this current loop in its initial position? A) +x B) x C) +y D) y z z .    x ●   LA y y X Right Hand Rule

Electricity & Magnetism Lecture 13, Slide 19 Calculation z z A square loop of side a lies in the xz plane with B B current I as shown. The loop can rotate about x 30˚. axis without friction. A uniform field B points along the +z axis. Assume a, I, and B are known. y y a I x final initial

What is the direction of the torque on this current loop in the initial position? A) +x B) x C) +y D) y

z B

y

Electricity & Magnetism Lecture 13, Slide 20 Calculation z z A square loop of side a lies in the xz plane with B B current I as shown. The loop can rotate about x 30˚. axis without friction. A uniform field B points along the +z axis. Assume a, I, and B are known. y y   a I U    B x final initial

What is the potential energy of the initial state?

A) Uinitial < 0 B) Uinitial  0 C) Uinitial > 0

z  0  B   90   B  0

  y

Electricity & Magnetism Lecture 13, Slide 21 Calculation z z A square loop of side a lies in the xz plane with B B current I as shown. The loop can rotate about x 30˚. axis without friction. A uniform field B points along the +z axis. Assume a, I, and B are known. y y   a I U    B x final initialinitial

What is the potential energy of the final state?

A) Ufinal < 0 B) Ufinal  0 C) Ufinal > 0

Check:  moves away from B z z initial final  1200 Energy must increase ! B B     90o   90o + 30o   B < 0 y y     U    B > 0

Electricity & Magnetism Lecture 13, Slide 22 Calculation z z A square loop of side a lies in the xz plane with B B current I as shown. The loop can rotate about x 30˚. axis without friction. A uniform field B points along the +z axis. Assume a, I, and B are known. y y   a I U    B x final initial

What is the potential energy of the final state?

3 1 A) U  Ia 2 B B) U  Ia 2 B C) U  Ia2B 2 2 z   1 1 o cos (120 )   U    B  Bcos (120 )  B 2 2 B   Ia2   120o 1 2 y U  Ia B  2

Electricity & Magnetism Lecture 13, Slide 23