physics 212 lecture 13, slide 1 physics 212 lecture 13 forces and torques on currents

Physics 212 Lecture 13, Slide Physics 212 Lecture 13, Slide 11

Physics 212Physics 212Lecture 13Lecture 13

Forces and Torques on Currents


Key Concepts:Key Concepts:

• Forces & Torques on loops of current Forces & Torques on loops of current due to a magnetic field.due to a magnetic field.

• The magnetic dipole moment.The magnetic dipole moment.

05


wireF I L B

Force on a wire carrying current I

Cross sectional area A, Length L

Number of charges/m3 = n

Each charge moving at Vavg

each avgF qv B

Force on each charge

wire each avgF N F Nqv x B

Total force on wire

avgqnAvInALN

Use

L

B

I

wireF

wireF I L B

L

Current- carrying wire in uniform B field

I

B

Out of page


F IL B

ACT

ABC

08


F IL B

ABC

ACT

10


F IL B

What is the force on section d-a of the loop?What is the force on section d-a of the loop?A)A) ZeroZeroB)B) Out of the pageOut of the pageC)C) Into the pageInto the page

ACT

12


Checkpoint 1a

13

ABC

“The net force on any closed loop is zero.”


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

A)A) Around the x axisAround the x axisB)B) Around the y axisAround the y axisC)C) Around the z axisAround the z axisD)D) It will not rotateIt will not rotate

x

y

15

Checkpoint 1b


R F

RF

Checkpoint 1c

17

ABCDE

y


Magnetic Dipole Moment

Area vectorMagnitude = AreaDirection uses right hand rule

Magnetic Dipole moment

turnsN IA

19


B

The torque always wants to lineThe torque always wants to line up with up with BB ! !

BB

B turnsturns toward toward BB

x

y

z

BB

B turnsturns toward toward BBx

y

z

21


B

B

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

I

BB

B

x

y

z

is up (turnsis up (turns toward B)toward B)

22

Practice with and


B

Biggest when B

24

Checkpoint 2aThree 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?


Potential energy of a magnetic dipole moment

2 2

2

1

1 1

2 1 sin cosBU U d B d B

27

U B

B

1

B

2Rotate from 1 to 2

2 1 2 1 2 1cos cosU U B B B B

Lowest U parallel to B

Highest U antiparallel to B

-1.5

-1

-0.5

0

0.5

1

1.5

0 30 60 90 120 150 180

B

U

U = 0


U B

Checkpoint 2b

30

U = 0 U = -Bcos

U = +Bcos

Three different orientations of a magnetic dipole moment in a constant magnetic field are shown below. Which orientation has the most potential energy?


ACT

30

c

a

a

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.

B

First, consider rotating to position c. What are the signs of the work done by you and the work done by the field?

A)Wyou > 0, Wfield > 0B)Wyou > 0, Wfield < 0C)Wyou < 0, Wfield > 0D)Wyou < 0, Wfield < 0

• U > 0, so Wfield < 0. Wyou must be opposite Wfield

• Also, torque and displacement in opposite directions Wfield < 0

fieldW U


ACT

30

c

a

a

Consider rotating the dipole to each of the three final orientations shown.

B

Does the sign of the work done by you depend on which position (a, b, or c) the dipole is rotated to?

A)YesB)NoThe lowest potential energy state is with dipole parallel to B. The potential energy will be higher at any of a, b, or c.

U B


CalculationCalculationA square loop of side a lies in the x-z plane with current I as shown. The loop can rotate about x axis without friction. A uniform field B points along the +z axis. Assume a, I, and B are known.

How much does the potential energy of the system change as the coil moves from its 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

z

x

y

B .30˚

y

z

Iinitial final

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

a

B

32


CalculationCalculation

• What is the direction of the magnetic moment of this current loop in its initial position?

(A) (A) +x (B) (B) -x (C) (C) +y (D) (D) -yz

x ●●y

A square loop of side a lies in the x-z plane with current I as shown. The loop can rotate about x axis without friction. A uniform field B points along the +z axis. Assume a, I, and B are known.

z

x

y

B .30˚

y

z

Iinitial final

a

B

IA

z

y

.

X

Right Hand Rule34



• What is the direction of the torque on the current loop in the initial position?

(A) (A) +x (B) (B) -x (C) (C) +y (D) (D) -y


z

x

y

B .30˚

y

z

Iinitial final

a

B

Bz

y

.

X

36



U B

• What is the potential energy of the initial state? (A) (A) Uinitial < 0 < 0 (B) (B) Uinitial = 0 = 0 (C) (C) Uinitial > 0 > 0

090


z

x

y

B .30˚

y

z

Iinitial final

a

B

z

y

B

38

0 B



• What is the sign of the potential energy in the final state? (A) (A) Ufinal < 0 < 0 (B) (B) Ufinal = 0 = 0 (C) (C) Ufinal > 0 > 0


z

x

y

B .30˚

y

z

Iinitial final

a

B

initial final z

y

B

z

y

B

U B

40

0120

U B

0 B

Check: moves away from B

Energy must increase !



2U Ia B(A) (B) (C) (A) (B) (C)

• What is the potential energy of the final state?


z

x

y

B .30˚z

Iinitial final

a

B

1cos(120 )2

oU B B B z

y

B

1cos(120 )2

o

U B

212

U Ia B

2Ia

212

U Ia B44

BIaU 2

23

physics 212 lecture 13, slide 1 physics 212 lecture 13 forces and torques on currents

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