ch29-magnetic fields-.pdf

Magnetic Fields

Dr.Hikmat Hamad

11/27/2014 1PHY201 Dr.Hikmat Hamad

Magnetic Poles

Every magnet, regardless of its shape, has two poles. Called north and south poles Poles exert forces on one another

Similar to the way electric charges exert forces on each other Like poles repel each other

N-N or S-S

Unlike poles attract each other N-S


Magnetic Poles, cont.

The force between two poles varies as the inverse square of the distance between them.A single magnetic pole has never been isolated.

In other words, magnetic poles are always found in pairs.

All attempts so far to detect an isolated magnetic pole has been unsuccessful.

No matter how many times a permanent magnetic is cut in two, each piece always has a north and south pole.


Magnetic Field LinesIron filings are used to show the pattern of the magnetic field lines.


Magnetic Fields and Forces The direction of the magnetic field at any location is the

direction in which a compass needle points at that location.


Magnetic Forces Properties of the magnetic force on a charged particle

moving in a magnetic field

We can define a magnetic field at some point in space in terms of the magnetic force the field exerts on a charged particle q moving with a velocity v , which we call the test object.

We can summarize all the observations of the magnetic force on a charged particle by writing the magnetic force in the form


Magnetic Forces-Cont

The magnitude of the magnetic force on a charged par ticle is


Force Direction: Right-Hand Rule

From the above Equation, we see that the SI unit of magnetic field is the newton per

coulomb-meter per second, which is called

the tesla (T):


Quick Quiz An electron moves in the plane of this paper toward the top

of the page. A magnetic field is also in the plane of the page and directed toward the right. The direction of the magnetic force on the electron is

(a) toward the top of the page,

(b) toward the bottom of the page,

(c) toward the left edge of the page,

(d) toward the right edge of the page,

(e) upward out of the page,

(f) downward into the page.


More About Magnitude of FB

The magnitude of the magnetic force on a charged particle is FB = |q| v B sin .

is the smaller angle between v and B FB is zero when the field and velocity are parallel

or antiparallel = 0 or 180o

FB is a maximum when the field and velocity are perpendicular

= 90o


Differences Between Electric and Magnetic Fields

Direction of force The electric force acts along the direction of the electric field. The magnetic force acts perpendicular to the magnetic field.

Motion The electric force acts on a charged particle regardless of whether the

particle is moving or not. The magnetic force acts on a charged particle only when the particle is in

motion.

Work and kinetic energy The electric force does work in displacing a charged particle. The magnetic force associated with a steady magnetic field does no work

when a particle is displaced.

This is because the force is perpendicular to the displacement of its point of application.

The kinetic energy of a charged particle moving through a magnetic field cannot be altered by the magnetic field alone.


Notation Notes

When vectors are perpendicular to the page, dots and crosses are used.The dots represent the arrows coming out of the page.The crosses represent the arrows going into the page.

The same notation applies to other vectors.


Charged Particle in a Magnetic Field Now consider the special case of a positively charged particle moving in a

uniform magnetic field with the initial velocity vector of the particle perpendicular to the field.

Lets assume the direction of the magnetic field is into the page .

The particle moves in a circle because themagnetic force is perpendicular to and and has a constant magnitude qvB.


Force on a Charged Particle


Applications Involving Charged ParticlesMoving in a Magnetic Field and Electric Field

A charge moving with a velocity in the presence of both an electric field and a magnetic field experiences both an electric force q and a magnetic force q x

The total force (called the Lorentz force) acting on the charge is

Velocity Selector


The Mass Spectrometer

A mass spectrometer separates ions according to their mass-to-charge ratio.

from which we can solve for m / q, Knowing the charge (ionized state) and the measured radius we can find the mass of the particle


Thomsons apparatus for measuring e/me.


Thomsons apparatus for measuring e/me. Cont

Thompsons experiment was an exceptionally clever combination of known electron acceleration and magnetic steering.


Thomsons e/m Experiment

-

The most precise value of e/m available as of this writing is


Helix Motion If a charged particle moves in a uniform magnetic field with its

velocity at some arbitrary angle with respect to B its path is a helix

Any component of the velocity of the charge parallel (or antiparallel) to the magnetic field will not be affected and the charge will move in a helix


Magnetic Force on a Current Carrying Conductor


Force on a Wire, equation

The magnetic force is exerted on each moving charge in the wire.

dq= F v B

The total force is the product of the force on one charge and the number of charges.

In terms of the current, this becomes


Force on a Wire, Arbitrary Shape

Consider a small segment of the wire,

The force exerted on this segment is

The total force is

ds


Example: 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 in Figure 29.20. Find the magnitude and direction of the magnetic force acting on the straight portion of the wire and on the curvedstraight portion

curved part


Torque on a Current LoopThe rectangular loop carries a current I in a uniform magnetic field.No magnetic force acts on sides 1 & 3.

The wires are parallel to the field and

0 =L B

There is a force on sides 2 & 4 since they areperpendicular to the field.

The magnitude of the magnetic force on these sideswill be:

F2 = F4 = I a B

The direction of F2 is out of the page.The direction of F4 is into the page.


Torque on a Current Loop, Equation

The forces are equal and in opposite directions, but not along the same line of action.The forces produce a torque around point O.

The maximum torque is found by:

This maximum value occurs only when the field is parallel to the plane of the loop.


Torque on a Current Loop, General

Assume the magnetic field makes an angle of < 90o with a line perpendicular to the plane of the loop.The net torque about point O will be

= IAB sin .

is perpendicular to the plane of the loop and has a magnitude equal to the area of the loop.

A


Magnetic FieldsDr.Hikmat HamadMagnetic PolesMagnetic Poles, cont.Magnetic Field LinesMagnetic Fields and ForcesMagnetic ForcesMagnetic Forces-ContForce Direction: Right-Hand RuleQuick QuizMore About Magnitude of FBDifferences Between Electric and Magnetic FieldsNotation NotesCharged Particle in a Magnetic FieldForce on a Charged ParticleApplications Involving Charged ParticlesMoving in a Magnetic Field and Electric FieldThe Mass SpectrometerThomsons apparatus for measuring e/me.Thomsons apparatus for measuring e/me. ContThomsons e/m ExperimentHelix MotionMagnetic Force on a Current Carrying ConductorForce on a Wire, equationForce on a Wire, Arbitrary ShapeExample: Force on a Semicircular ConductorTorque on a Current LoopTorque on a Current Loop, EquationTorque on a Current Loop, General

ch29-magnetic fields-.pdf

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