Chapter 27 Motion of Charged Particles in a Magnetic Field

Electricity and MagnetismElectricity and Magnetism

27 Motion of Charged Particles in a Magnetic Field

Chapter 27

Motion of Charged Particles in a Magnetic Field



• In the presence of electric field, the electrons experience

electric forces and drift slowly in the opposite direction of the

electric field at the drift velocity.• The drift velocity (~10–5 m s–1) of free electrons is extremely

small compared with their mean speed (~106 m s–1).



• The current I carried by a conductor can be expressed as

where n is the number of free charge carriers per unit volume;

A is the cross-sectional area of the conductor;

v is the drift velocity of the charge carriers;

Q is the charge carried by the charge carriers.

Example 27.1

I = nAvQ

Microscopic view of electric current Checkpoint (p.319) O



27.2 Magnetic force on a moving charge

• The magnetic force F on a moving charged particle with a

velocity v in a magnetic field B at an angle is given by

F = BQv sin

The direction of the force can be determined by Fleming’s left hand rule.

Q → +ve

= 90˚Q → –ve

= 90˚

≠ 90˚

Example 27.2

Experiment 27.1



• To pass through the crossed fields in a velocity selector

without deflection, the speed of the particles must be

Example 27.3Velocity selectorCheckpoint (p.326) O

B

Ev



• The motion of a charged particle in a uniform magnetic field B

depends on the angle between its initial velocity v and the

direction of the field. = 0° or 180°

rectilinear motion

F = 0

Motions of charged particles in uniform magnetic field



BQvr

mv

2

The centripetal force is provided by the magnetic force acting on the particle:

QB

mvr

• The motion of a charged particle in a uniform magnetic field B

depends on the angle between its initial velocity v and the

direction of the field. = 90° circular motion



• In a mass spectrometer, the radii of the semi-circular paths

taken by the charged particles depend on their charge to

mass ratios, so that different particles can be separated and

identified.

QB

mvr

Recall that the radius r of the circular path is given by

The radius r differs if the charge to mass ratios (Q / m) differs.

Example 27.4Mass spectrometerCheckpoint (p.330) O



27.3 Hall effect

• When a current passes through a conductor placed in a unifo

rm magnetic field, each of the charge carriers experiences a

magnetic force and deflects to the surfaces.

A conductor with positive charge carriersA conductor with negative charge carriers

Deflection of charge carriers in conductor



• The deflection of the moving charged carriers leads to

– an excess of positive (or negative) charge carriers on the

upper surface, and

– a deficiency of positive (or negative) charge carriers on

the lower surface.

A conductor with positive charge carriers

A conductor with negative charge carriers



• A p.d. is developed across the conductor due to the deflected

charge carriers.• Each charge carrier moving in the conductor experiences an

electric force that opposes the magnetic force on it.• These two forces balance each other in the steady state.

Hall voltage

A conductor with positive charge carriers

A conductor with negative charge carriers



• The Hall effect is the production of a Hall voltage across the

opposite surfaces of a current-carrying conductor placed in a

magnetic field, which is given by

nQb

BIV H

Example 27.5

VH

Checkpoint (p.338) O

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Chapter 27 Motion of Charged Particles in a Magnetic Field