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Magnetic Fields CHAPTER OUTLINE 29.1 Magnetic Fields and Forces
29.2 Magnetic Force Acting on a Current-Carrying Conductor 29.4 Motion of a Charged Particle in a Uniform Magnetic Field 29.5 Applications Involving Charged Particles Moving in a Magnetic 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 per
coulomb-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 into the paper are indicated by crosses, representing the feathers of arrows going inward.

Magnetic Force Acting on a Current-Carrying Conductor
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,

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 curved portion. 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 Uniform
Magnetic Field consider a positively charged particle moving in a uniform magnetic field with the initial velocity vector of the particle perpendicular to the field. 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 Particles
Moving 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

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