Chapter 26: Magnetism, Force and Field Tuesday October 11th

• Review of Mini Exam 3 • Brief history of magnetism • Forces on moving charges

• The Lorentz force • Velocity, momentum and mass detectors • Cyclotron motion

• The force on a current carrying wire • Torque on a current loop (if time)

Reading: up to page 442 in the text book (Ch. 26)

Cumulative mid-term exam next Thursday In-class – 75 minute, written exam

Magnetic Field

The compass 1000 AD

The Magnetic Field The ‘Gilbert Model’ (William Gilbert - 1600)

Like poles repel, and unlike poles attract.

1820 - Electromagnetism, Current In 1820, a physicist Hans Christian Oersted, learned that a current flowing through a wire would move a compass needle placed beside it. This showed that an electric current produced a magnetic field.

The Magnetic Field

I

I

Ampere: magnetic force between two wires

F21= I

2LB

1= I

2LµoI1

2!d

!F21= I

2

!L!!B1

µo= 4!!10"7 T #m/A

chosen so that when I1 = I2 = 1 A, and L = d = 1 m, F21 = 2×10-7 N µo

I1

I2

Also 1820

v, I

v, I

F+!=

!2"#

od"!L

#

$

%%%

&

'

(((

v2

c2

)

*++++

,

-.....=

I2!"

oc2d

)

*

+++++

,

-

.....IL = BIL; B =

µoI

2!d;

1c2= µ

o!

o

Connection to Relativity

r

L Because + and – charges move at different speeds, the electrostatic force between them is modified by an amount v2/c2

Magnetic Forces Act on Moving Charges

3. The magnetic force is always perpendicular to the velocity of the test charge (magnetic forces do no work!).

3. The magnetic force also depends on the direction of the velocity relative to certain fixed axes - being zero in one direction and maximum perpendicular to this direction.

1. The magnitude of the force is proportional to the velocity. 2.  The magnitude of the force is proportional to the charge.

q

Experimental facts:

We define the magnetic field:

B =FB,max

q v, or F

B= q vB sin!

In fact: !FB= q!v!!B

1tesla=1newton

coulomb!meter/second=1

newtonampere!meter

q

Magnetic Forces Act on Moving Charges

The Lorentz Force !F = q

!E+

!v!!B( )"

#$%&'

The Cathode Ray Tube (CRT)

Cyclotron Motion

v

B

Uniform magnetic field

q

F

•  Force is perpendicular to v, so it can do no work •  Consequently, v is a constant of the motion •  Since q, B and v are constant, then so is F •  Consequently, trajectory is a circle in plane ! B

The Lorentz Force

• The velocity filter: EvB

=(undeflected trajectories in crossed E and B fields)

• Cyclotron motion:

FB=ma

r! q vB =m

v2

r

r =mv

q B=p

q B

! = 2!f =q B

m

K = 12mv2 =

q 2B2R2

2m

• Orbit radius:

• Orbit frequency:

• Orbit energy:

momentum (p) filter

mass detection

The Magnetic Force on a Current-Carrying Wire

!F

B= I!L!!B

= ILB sin!

I I

I

B into page