1 / 22

Chapter 29 Magnetic Fieldscontinued

- PHYS 2326-16

Electromagnetic Force

- on a moving charge

Electric Magnetic Force Differences

- Force for electric field is along the direction

of the field line, force for magnetic field is

perpendicular to the field - Electric field force operates on any charge,

Magnetic field force acts only on moving charge - Electric field performs work when displacing

charged particle, Magnetic field moves charges

perpendicular to displacement performing no work.

Right Hand Rule

Right Hand Rule

- Cross product reverses sign when reverse vectors

v x B -B x v - Result is perpendicular to the plane that

contains v and B. - Direction for result F is the same as a screw

moves when rotated in the direction from v to B

(clockwise moves screw in and CCW moves screw out

Charged Particle in Uniform Field

- Magnetic force F is perpendicular to v and B
- Has constant magnitude qvB.
- Motion is in a circle for uniform B and no other

forces acting on the moving charged particle - centripetal acceleration force mv2/r
- r mv/qB (top is momentum) eqn 29.3
- ? v/r qB/m angular speed
- T2pr/v 2 p/ ? 2 pm/ qB period

Cyclotron Frequency

- Cyclotron frequency is ? the angular speed
- A cyclotron is an essentially obsolete particle

accelerator mostly now used in nuclear

medicine. - If there is a velocity component parallel to B

there is no effect on the particle due to this

component and the path becomes a helix

Cyclotron

- Atom smasher
- Hollow cylinder in 2 insulated halves with a

uniform magnetic field along the cylinder axis. - Particles released near the center
- The two halves flip flop an E field drawing

particles from one side to the other and back

imparting kinetic energy each time qV - Particle spirals out with increased speed
- Exits when fast enough to reach exit point

Velocity Selector

- An apparatus where there is an electric field

perpendicular to a magnetic field and both

perpendicular to the initial motion of a stream

of charged particles one can create a velocity

selector. - FB qvB (direction right hand rule)
- FE qE (direction E)
- FB - FE (- is opposite directions)
- qE qvB so that v E/B (magnitude)
- Particles with velocity v go through undeflected,

others are diverted

Mass Spectrometer

- Separates ions according to mass / charge ratio
- Bainbridge mass spec. beam enters a velocity

separator then through a perpendicular magnetic

field B - Ions move in semicircle striking the detector at

a point P. Negative ions are deflected one way,

positive the other.

Mass Spectrometer Equations

- Starting with 29.3 the radius eqn rmv/qBo for

uniform and perpendicular motion and Bo field. - m/q Bo r/v by rearranging
- substituting 29.7 the velocity selector equation,

vE/B - m/q r Bo B/E

Chapter 29 Magnetic Forces on Currents

- PHYS 2326-17

Concepts to Know

- Magnetic Force on a Current Element
- Magnetic Dipole
- Magnetic Dipole Moment
- Magnetic Torque on a current loop
- Solenoid

Why Magnetics Might be Important during Your

Careers

- Control and automation of ????
- Rail guns magnetic propulsion of material
- Magnetic levitation trains, transport
- Electric/hybrid vehicle design
- Fusion power generation containment
- EMP protection
- Your latest electric kitchen gizmo invention to

be peddled by Ronco

Magnetic Field

- Vector B represents the magnetic field with a

direction from N-pole to S-pole - Unit is Tesla
- alternate unit is Gauss 10-4 typical earth

field 0.5 Gauss - North pole of magnets attracted earths north

pole which is opposite polarity

Solenoid

- A solenoid is a coil of wire wrapped as a helix
- It also refers to a device that uses an

electromagnet to switch something on or off - A relay is a solenoid device for switching an

electric circuit on/off. - A solenoid may actuate a valve for liquids or

gases to permit or block flow

Magnetic Force on a Current Element

- Current is free charges moving with the drift

velocity vd. - I n q vd A

Magnetic Force on a Current Loop

- See Example 29.4
- Conclusions for uniform field are
- Force on conductor depends only on end points
- Net magnetic force on closed current loop is zero

Magnetic Torque

- Given a current carrying loop of 4 sides
- Sides 13 are parallel to field no effect
- Sides 24 are perpendicular to field

Side View

Top View

1

F

A

a

I

x

2

.

4

F

b

B

B

3

Magnetic Torque

For a Solenoid

- A solenoid is a coil of wire with more than 1

turn - Âµ N I A magnetic dipole moment for a coil of

N turns, I amperes and area A

Potential Energy of Magnetic Dipole