• When charged particles move through magnetic fields, they experience a force, which deflects them

• Examples of such particles are electrons, protons, and alpha particles

Uncharged (neutral) objects are not deflected by magnetic or electric fields

• The magnitude of the force on the particle depends on the magnetic field strength, the charge on the particle and the velocity (magnitude and direction) of the particle

qvBFm

Indicates that the field is at right angles to the direction of motionB

• The magnetic force on the particle is zero if the particle is going parallel to the magnetic field

If the direction of travel (v) is at right angles to the magnetic field vector, the resulting force is perpendicular to BOTH v and B

The magnetic force deflects the charged particles from a straight line but doesn't cause them to change their speed, the magnetic field does no work on the charges.

Example Problem:Determine the magnitude and direction of the magnetic force on a proton moving horizontally to the north at 8.6 x 104 m/s, as it enters a magnetic field of 1.2 T, pointing vertically upward.

(1.7 x 10-14 N, east)

3RD HAND RULE (forces on charges)• Thumb in direction of charge motion• Fingers point in the field direction (toward south pole)• Palm indicates the direction of the magnetic force on the charged particles

v

+

v

-

Use left hand for negative charges

Use right hand for positive charges

• If a current carrying conductor is placed in a perpendicular magnetic field, a force will be exerted on the conductor

ILBFmI = current in wireL = length of wire at right angles to field = magnetic field perpendicular to wire

If the wire is parallel to the magnetic field, no magnetic force is exerted on the wire

B

to the top of the page

Examples 1.Determine the direction of the magnetic force for each of the following diagrams. The direction of electron current is out of the page.

to the bottom of the page

to the left to the right

2. A wire carries an electron current of 15 A through a perpendicular magnetic field as shown below. Determine the magnitude and direction of the magnetic force acting on the wire.

F = (15 A)(0.20 m)(0.25 T) = 0.75 N to the right side of the page.

CIRCULAR MOTION OF CHARGES •In a large, strong perpendicular magnetic field the charged particles will go in a circle, or portion of a circle

• The centripetal force is always toward the centre of the circle and is caused by the magnetic force

A negative charge:

•The radius of the circle can be found by setting Fm = Fc

qBmvr

mvqBrmvqvBr

rmvqvB

2

2

• Charged particles from the sun and outer space become trapped in a part of the earth’s magnetic field (called the Van Allen belts) and move toward the poles

• Near the poles the particles collide with gas molecules and raise the energy of the molecules which then emit light (northern and southern lights)

Example problems3) Calculate the magnitude and direction of the magnetic force acting on a proton traveling north at 3.52 x 105 m/s through a magnetic field of 0.280 T, if the magnetic field is directed upward.

1.58 x 10-14 N, east

4) What is the acceleration (magnitude and direction) of an electron that is traveling east at 8.30 x 104 m/s through a 0.310 T magnetic field directed south?

F = 4.12 x 10-15 Na = 4.52 x 1015 m/s2 up

5) A proton falls from rest through a potential difference of 3.34 x 105 V. It then enters a region perpendicular to a 0.0200 T magnetic field. How large is the radius of the path?

4.18 m

6) A beam of charged particles is accelerated from rest to a speed of 2.50 x 106 m/s and moves into a 6.50 x10-2 T magnetic field where the particles are deflected by into a 0.803 m radius path. Identify the particles using the charge to mass ratio (q/m). This is the basis of the Thomson experiment.

mvqBrmvqvBr

rmvqvB

2

2

kgCxm

q

mT

smmq

Brv

mq

/7107897.4

803.021050.6

/61050.2

Fm =

Fc

q/m for electron = 1.756x1011 C/kgq/m for proton = 9.5808x107 C/kgq/m for alpha particle = 4.776x107 C/kg

A Mass Spectrometer: