Today’s Concept:Torques in Magnetic Fields

Physics 2112Unit 13

Unit 13, Slide 1

Last Time:

F qv B

yz

x

BF

I

This Time:BvqF

ii

BvqNF avg

BLIF

avgqnAvI

nALN

Unit 13, Slide 2

Force on current carrying wire

Unit 13, Slide 3

Example 13.1 (Force on Wire)

BLIF

X X X X X X X

X X X X X X X

X X X X X X X

X X X X X X X

X X X X X X X

I

0.5m

A wire is carrying 5amps through a magnetic field that is 50cm long and has a strength of 12 Gauss.

What is the force on the wire?

Value of Torque

.Q

z

final

B|t| = 2*(W/2)*sin(Q)*(B*L) = W*L*B*sin(Q)

= (Area of Loop)*B*sin(Q)

W

Magnetic Dipole Moment

Define: Area vectorMagnitude = AreaDirection uses R.H.R.

Define: Magnetic Dipole moment

ANI

Unit 13, Slide 5

m Makes Torque Easy!

The torque always wants to line m up with B!

B

Bm

turns m toward B

x

y

z

B

B

m

turns m toward Bx

y

z

B

“Dipole moments, I don't get how they are different from torques”

Dipole moments tell you how much torque a given B field will place on a loop. |t| = |m||B|sinq

Unit 13, Slide 6

Example 13.2 (Torque on Loops)

5A of current is moving clockwise through 20 loops of copper wire. The loops have a radius of 50cm and are placed in a 500 Gauss magnetic field as shown to the right.

What is the torque on the loop?

Unit 13, Slide 7

Magnetic Field can do Work on Current

From Physics 2111:

From Physics 2112: sin( )B B

dW

Define U = 0 at position of maximum torque

BU

-1.5

-1

-0.5

0

0.5

1

1.5

0 30 60 90 120 150 180

Bm

WU

BBdBW

)cos()sin(

Unit 13, Slide 8

CheckPoint 2A

B

Biggest when B

Unit 13, Slide 9

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 ?

CheckPoint 2B

Unit 13, Slide 10

Which orientation has the most potential energy?

BU

CheckPoint 2C

Unit 13, Slide 11

In order to rotate a horizontal magnetic dipole to the three positions shown, which one requires the most work done by the magnetic field?

How much does the potential energy of the system change as the coil moves from its initial position to its final position.

Conceptual AnalysisA current loop may experience a torque in a constant magnetic field

t = m X BWe can associate a potential energy with the orientation of loop

U = - m ∙ B

z

x

y

B .30˚

y

z

I

initial final

Strategic AnalysisFind mCalculate the change in potential energy from initial to final

a

B

Example 13.3 (Rotating Loop)

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.

Unit 13, Slide 12

Remember?

BU mag

Bmag

EU elec

Eelec

Electric Dipoles

+

-

dqelec

Magnetic Dipoles

ANImag

What’s all this good for?

Many things. I’ll mention two…..one every day…..one high tech

X

.

What if when it reaches this point, you reverse the direction of the current in the coil?

X.

Electric Motor

MRI

Protons have charge and spin…have magnetic moment

m Place in strong B field and m will try to align with field.

Will precess like top in gravity field (…remember from 2111?)

Look for the signal from the precession and can spot protons in hydrogen

Hydrogen is in water which is in soft tissueMagnetic Resonance Imaging (MRI)