CH 8: Magnetic Fields

8.4 – Motion of Charged Particles in Magnetic Fields

Agenda Warm Up / Homework Check

Clicker Questions from yesterday

Lesson on Section 8.4

Textbook Questions

Learning Goals Analyse and solve problems involving

the motion of charged particles in magnetic fields

Warm Up QuestionA 155mm part of a wire has a mass of 0.30kg and carries an electric current of 3.5 A. The conventional current passes through a uniform magnetic field of 2.5 T. The direction of the wire and the magnetic field are shown in Figure 7. A. What is the magnitude of the magnetic

force on the wire?B. Use the right-hand rule to determine

the direction of the magnetic force.

Warm Up QuestionEarth’s magnetic field exerts a force of 1.4 x 10-5 N on a 5 cm segment of wire in a truck motor. The motor wire is positioned at an 23° angle to Earth’s magnetic field, which has a magnitude of 4.9 x 10-5 T at the truck’s location. Calculate the current in the wire.

4. Clicker Question

5. Clicker Question

7. Clicker Question

8. Clicker Question

9. Clicker Question

Mass Spectrometerhttp://www.youtube.com/watch?v=_L4U6ImYSj0

Motion of a Charged Particle in a Magnetic Field

v

F

F

v

v

v

F

Magnetic force provides the centripetal acceleration.

Motion of a Charged Particle in a Magnetic FieldIf m, q and B are held constant, higher speed larger radius.

106 m/s F1

2x106 m/s F

2

r

2r

ExampleA Bainbridge mass spectromoter is used to measure the mass of zinc ions (Zn+). The ions enter a magnetic field, of strength B=1.8T with a speed of 4.2 x 104 ms-1 and they move in a circular path of radius r = 1.7cm. What is the mass of the zinc ions?

An electron in a magnetic FieldAn electron starts from rest. A horizontally directed electric field accelerates the electron through a potential difference of 40V. The electron then leaves the electric field and moves into a magnetic field. The magnetic field strength is 0.T, directed into the page (Figure 3), and the mass of the electron is 9.11 x 10-31 kg.

A. Determine the speed of the electron at the moment it enters the magnetic field.

B. Determine the magnitude and direction of the magnetic force on the electron.

C. Determine the radius of the electron’s circular path.

Mass Spectrometer: Separating Isotopes

Cyclotron Particle Accelerator http://

www.youtube.com/watch?v=cNnNM2ZqIsc

TRIUMF National laboratory in Vancouver has the largest cyclotron at 18m

Use of Magnetic Fields in Cyclotrons

Particles moving in a cyclotron are subjected to a uniform magnetic field which causes the particles to move in a circular path.Each time the charged particle enters a Dee it follows a semi-circular path and each time it traverses to the other Dee its speed is greater than before as it is subjected to an Electric field. Its energy has increased by W=qV.

Use of Magnetic Fields in Cyclotrons

The period of the charged particle is independent of its speed, this can be shown by the following,

qBmt

qBm

rqBrmt

mrqBv

qBmvr

vrt

rrC

2

revolution full one complete taken totime

thus

but

semicircle one traverse totime)semicircle one oflength ( 2

circle, a of nceCircumfere

Use of Magnetic Fields in Cyclotrons

The Kinetic Energy can be found by,

mrBq

qBmvr

mrqBm

mvEk

2

as

222

2

21

22

1

Use of Magnetic Fields in Cyclotrons

Example, A cyclotron is used to accelerate dueterons (q = 1.6 x 10-19C) of

mass 3.34 x 10-27 kg. The radius of the cyclotron is 30cm and the magnetic field applied to it has strength 1.6T. Find

(a)The period of the particles in their circular path.(b)The energy (in eV) of the particles leaving the cyclotron.

Use of Magnetic Fields in Cyclotrons

(a)The period of the particles in their circular path.

s

qBmT

8

19

27

102.8 6.1106.1

1034.32

2

Use of Magnetic Fields in Cyclotrons

(b) The energy (in eV) of the particles leaving the cyclotron.

MeVeV

J

mrBqK

52.5 1052.5

106.1108.83

eV into change1083.8

1034.32)3.0()6.1()106.1(

2

6

19

13-

13

27

22219

222

Homework

pg. 404 #2-6Quiz on Chapter 8 Tomorrow?