Physics 2112Unit 12

Today’s Concept:Magnetic Force on Moving Charges

BvqF

Unit 12, Slide 1

Magnetic Force

BvqF

Unit 12, Slide 2

Electric Field• Any particle can cause E field• Any particle affected by E field

Magnetic Field• Only moving particle can cause B field• Only moving particle affected by B field

Units

Unit 12, Slide 3

• Earth ~ 0.6 Gauss• Frig Magnet ~ 0.01T (100 Gauss)• MRI 1.5 ->5.0 Tesla (15,000 – 30,000 Gauss)• LHC 8.4 Tesla• World’s Record 45 Tesla (National High

Magnetic Field Laboratory at Florida State)

Units: Telsa (N/(Cm/sec))

Extremely large field so sometimes use Gauss = (10-4T)

Cross Product Review

Cross Product different from Dot Product

is a scalar; is a vector proportional to the component of B parallel to A proportional to the component of B perpendicular to A

Definition of Magnitude: |A||B|sinq

Direction: perpendicular to plane defined by A and B with sense given by right-hand-rule

Unit 12, Slide 4

BA

BA

BA

BA

BA

xy

z

BF

qv

Remembering Directions: The Right Hand Rule

BvqF

Unit 12, Slide 5

Example 12.1 (Acceleration of proton)

Unit 12, Slide 6

The earth’s magnetic field is pointed roughly 70o from the horizontal in Chicago.

What would the acceleration of a proton be if it were moving at 1% of the speed of light in the horizontal direction?

CheckPoint 2

Three points are arranged in a uniform magnetic field. The B field points into the screen.

Unit 12, Slide 7

A positively charged particle is located at point A and is stationary.

The direction of the magnetic force on the particle is:

A. right B. left C. into the screen D. out of the screen E. zero

CheckPoint 3

Three points are arranged in a uniform magnetic field. The B field points into the screen.

Unit 12, Slide 8

Now the positive charge moves from point A toward B.

The direction of the magnetic force on the particle is:

A. right B. left C. into the screen D. out of the screen E. zero

Motion of Charge q in Uniform B Field

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

x x x x x x x

Uniform B into page

Force is perpendicular to vSpeed does not changeUniform Circular Motion

Solve for R:

R

Demo

qvBFBvqF

R

va

2

R

vmqvB

2

q

q q

v

F

v

F

v

F

v

F

q

qB

mvR

Unit 12, Slide 9

Example 12.2 (Analysis Magnets)

Unit 12, Slide 10

A proton enters the magnetic field of an analysis magnet at Fermilab and it deflected by an angle of Q = 10o. The field has a strength of 0.2T and a length of 2meters. What is the speed of the incoming proton?

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

Q

X X X X X X X

X X X X X X XQ R sinQ

Follow up

Unit 12, Slide 11

The analysis magnet

Photograph of track in bubble chamber (pre

1984)

Electronic version of

same thing (top quark

event at CDF)

Question: In the previous example how did you know it was a proton?