Magnetic FieldsMagnetic FieldsMagnetic FieldsMagnetic FieldsCHAPTER OUTLINECHAPTER OUTLINE

29.1 Magnetic Fields and Forces29.1 Magnetic Fields and Forces

29.2 Magnetic Force Acting on a29.2 Magnetic Force Acting on a

Current-Carrying ConductorCurrent-Carrying Conductor

29.4 Motion of a Charged Particle29.4 Motion of a Charged Particle

in a Uniform Magnetic Fieldin a Uniform Magnetic Field29.5 Applications Involving

Charged Particles Moving in aMagnetic Field

29.1 Magnetic Fields and Forces

Experiments on various charged particles moving in a magnetic field give the following results:

We can summarize these observations by writing the magnetic force in the form

Right-hand rules for determining the direction of the magnetic force

The magnitude of the magnetic force on a charged particle is

FB is zero when v is parallel or antiparallel to B (Ɵ= 0 or 180°) and maximum when v is perpendicular to B (Ɵ= 90°).

The SI unit of magnetic field is the newton percoulomb-meter per second, which is called the tesla (T):

Example 29.1 An Electron Moving in a Magnetic Field

(B) Find a vector expression for the magnetic force on the electron

29.2 Magnetic Force Acting on a Current-Carrying Conductor

The direction of magnetic field

Magnetic field lines coming out of the paper are indicated by dots, representing the tips of arrows coming outward.

Magnetic field lines going intothe paper are indicated by crosses,representing the feathers of arrowsgoing inward.

considering a straight segment of wire of length L and cross-sectional area A, carrying a current I in a uniform magnetic field B, as shown in Figure. The magnetic force exerted on a charge q moving with a drift velocity vd is

nAL is the number of charges in the segment.

We can write this expression in a more convenient form by noting that, from Equation 27.4, the current in the wire is I = nqvdA. Therefore,

Magnetic Force Acting on a Current-Carrying Conductor

where L is a vector that points in the direction of the current I and has a magnitude equal to the length L of the segment. Note that this expression applies only to a straight segment of wire in a uniform magnetic field.

Example 29.2 Force on a Semicircular Conductor

A wire bent into a semicircle of radius R forms a closed circuit and carries a current I. The wire lies in the xy plane, and a uniform magnetic field is directed along the positive y axis, as shown in Figure. Find the magnitude and direction of the magnetic force actingon the straight portion of the wire and on the curvedportion.

The magnetic force F acting on the straight portion has a magnitude F = ILB = 2IRB because L = 2R.

29.4 Motion of a Charged Particle in a UniformMagnetic Field

consider a positively charged particle moving in a uniform magnetic field with the initial velocity vector of the particle perpendicular to thefield. Let us assume that the direction of the magnetic field is into the page, as in Figure. As the particle changes the direction of its velocity in response to the magnetic force, the magnetic force remains perpendicular to the velocity. If the force is always perpendicular to the velocity, the path of the particle is a circle.

r is the radius of the path

the radius of the path is proportional to the linear momentum mv of the particle and inversely proportional to the magnitude of the charge on the particle and to the magnitude of the magnetic field. The angular speed of the particle is

The period of the motion (the time interval the particle requires to complete one revolution) is equal to the circumference of the circle divided by the linear speed of the particle:

Example 29.6 A Proton Moving Perpendicular to a Uniform Magnetic Field

Example 29.7 Bending an Electron Beam

29.5 Applications Involving Charged ParticlesMoving in a Magnetic Field

A charge moving with a velocity v in the presence of both an electric field E and a magnetic field B experiences both an electric force qE and a magnetic force q vx B. The total force (called the Lorentz force) acting on the charge is