E N G I N E E R I N G P H Y S I C S SUBTOPICS S C - - PDF document

E N G I N E E R I N G P H Y S I C S

2011/2012

E N G I N E E R I N G P H Y S I C S

2011/2012

SUBTOPICS

• Magnets, magnetic poles and

magnetic field direction

• Magnetic field strength and magnetic

force

• Force and current-carrying conductor
• Magnetic material: Ferromagnetic

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When thinking about magnetism, most people tends to think of an attraction – certain things can be picked up with a magnet.

INTRODUCTION

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In physics, magnetism is

• ne
• f

the phenomena by which materials exert attractive

• r repulsive forces on other materials.

Materials that exhibit easily detectable magnetic properties (called magnets) are nickel, iron and their alloys; however, all materials are influenced to greater or lesser degree by the presence of a magnetic field. Magnetism also has other manifestations in physics, particularly as

• ne
• f

the two components of electromagnetic waves such as light.

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Magnetostatics is the study of static magnetic fields. In electrostatics, the charges are stationary, whereas here, the currents are stationary. As it turns out magnetostatics is a good approximation even when the currents are not static as long as the currents do not alternate rapidly.

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MAGNETS, MAGNETIC POLES AND MAGNETIC FIELD DIRECTION

Magnets have two distinct types

• f

poles; we refer to them as north (N) and south (S).

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By using two bar magnets, the nature of forces acting between them can be determined.

• pole – force law or law of poles: -

Like magnetic poles repel and unlike poles attract.

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T wo magnetic poles of opposite kind form a magnetic dipole. All known magnets are dipoles (or higher poles); magnetic monopoles could exist (in theory) but have never been observed (experimentally). A magnet creates a magnetic field B : The direction of a magnetic field (B) at any location is the direction that the north pole of a compass would point if placed at that location.

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North magnetic poles are attracted by south magnetic poles, so the magnetic field points from north poles to south poles. The magnetic field may be represented by magnetic field lines. The closer together (that is, the denser) the B field lines, the stronger the magnetic field. At any location, the direction of the magnetic field is tangent to the field line, or equivalently, the way the north end of a compass points.

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MAGNETIC FIELD STRENGTH AND MAGNETIC FORCE

A magnetic field B can exert a force on a moving charged particle.

A horseshoe magnet created by bending bar magnet, produces a fairly uniform field between its poles. When a charged particle enters a magnetic field, the particle is acted on by a force whose direction is

• bvious by the deflection of

the particle from its original path.

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The magnitude of the force is proportional to the particle’s charge and its speed. When the particle’s velocity v is perpendicular to the magnetic field B, the magnitude of the field is

valid only when v is perpendicular to B

Where, F is force and q is charges

SI unit of magnetic field: newton/ampere- meter (N/(A.m) or commonly used - tesla, T.

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In general, a particle’s velocity may not be perpendicular to the field. Then the magnitude of the force depends on the sine of the angle θ between velocity vector and the magnetic field vector, thus it may be represents as,

The force is perpendicular to both the velocity and to the field.

The magnetic force F = 0 when v and B is parallel (θ = 0° or 180°),

The maximum when v and B is perpendicular (θ = 90°), where

F = qvB sin (90°) = qvB

Magnetic force on charged particle NOTE:

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The right-hand Force Rule for moving charges A right-hand rule gives the direction of the force.

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EXAMPLE 1

The figure above shows three situations in which charged particle with velocity v travels through a uniform magnetic field B. In each situation, what is the direction

• f

the magnetic force FB on the particle?

+ y x z

• y

x z

• y

x z v B B v v B (a) (b) (c)

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EXAMPLE 2

A uniform magnetic field B, with magnitude 1.2 mT, points vertically upward throughout the volume of a laboratory chamber. A proton with kinetic energy 5.3 MeV enters the chamber, moving horizontally from south to

• north. What magnetic deflecting force acts on

proton as it enters the chamber? [the proton mass, m = 1.67 x 10^-27kg]

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Solution:

The magnetic deflecting force depends on the speed of the proton, which we can find from K = ½ mv2, solving for v, we find

kinetic energy ,k=1 2 mv

2

find velocity ,v v= 2k m = 25.3MeV1.60x 10

−13 J / MeV 

1.67x 10

−27 kg

v=3.2x10

7 m/s

using F 

B=qvBsin 

F 

B=1.60x10 −193.2x10 7m/ s1.2x10 −3T sin 90

• 

F 

B=6.1x10 −15 N

It may seem like a small force, but it acts on a particle of small mass, producing a large acceleration

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EXAMPLE 3

An electron propagates with velocity of 4 x 10^7 m/s perpendicular with B = 1.5 T

• esla. Calculate

the electron’s orbit radius? Where mass of electron,m = 9.11x10^-31 kg Solution:

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Applications: Charged Particles in Magnetic Fields

A cathode-ray tube, such as a television or computer monitor, uses a magnet to direct a beam of electrons to different spots on a fluorescent screen, creating an image.

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A velocity selector consists of an electric and magnetic field at right angles to each other. Ions entering the selector will experience an electric force: and a magnetic force: These two forces will be perpendicular to each other.

B E

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The magnetic force on a current-carrying wire is a consequence of the forces on the charges. The force on an infinitely long wire would be infinite; the force on a length L of wire is:

MAGNETIC FORCES ON CURRENT-CARRYING WIRES

θ is the angle between I and B.

If current, I, and magnetic field, B, is perpendicular to each other (θ = 90°), thus

F = ILB

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The direction of the force is given by a right- hand rule:

When the fingers of the right hand are pointed in the direction of the conventional current I and then curled toward the vector B, the extended thumb points in the direction of the magnetic force on the wire. Can you used “Left-Hand Rule”?

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Additional: Fleming’s Left-Hand Rule Fleming's left hand rule (for electric motors) shows the direction of the thrust (F) on a conductor carrying a current (I) in a magnetic field (B).

John Ambrose Fleming (1849 – 1949)

Named after British engineer John Ambrose Fleming who invented them.

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EXAMPLE 4

A straight, horizontal stretch of copper wire has a current I = 28A through it. What are the magnitude and direction of the minimum magnetic field B needed to suspend the wire, that is, balance its weight? Its linear density is 46.6 g/m.

mg FB B Length, L [side view]

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Solution:

The wire with length L, and the current is out of

• page. If the field is to be minimal, the force FB

that is exerts on the section must be upward. B to be horizontal. In order to balance the weight of the section, FB must have the magnitude FB = mg, then The direction of FB is related to the direction of B and wire's length, L, thus

iLBsin =mg find magnetic field B , B=mg iLsin 

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Solution:

B=46.6x 10

−3kg /m9.8 m/ s 2

28Asin 90

• 

B=1.6x10

−2T

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Applications: Current-Carrying Wires in Magnetic Fields

The Galvanometer: The Foundation of the Ammeter & Voltmeter

A galvanometer has a coil in a magnetic field. When current flows in the coil, the deflection is proportional to the current.

Sensitive Galvanometer Large Volt/Ampere Galvanometer

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The dc Motor An electric motor converts electric energy into mechanical energy, using the torque on a current loop.

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The Electronic Balance An electronic balance uses magnetic force to balance an unknown mass. The amount of current required is proportional to the mass.

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ELECTROMAGNETISM: THE SOURCE OF MAGNETIC FIELDS

Magnetic Field near a Long, Straight, Current-Carrying Wire

The magnitude of the field is given by: d is the distance B from current carrying wire The constant μ0 is called the permeability

• f free space.

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The field lines form circles around the wire; the direction is given by a right-hand rule.

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The magnetic field at the center of a current loop:

Magnetic Field at the Center of a Circular Current-Carrying Loop

For N loops

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A solenoid is a wire coiled into a long cylinder. The magnetic field inside is given by:

Magnetic Field in a Current-Carrying Solenoid

Magnetic field near the center

• f a solenoid.

Solenoid field Depends on how closely packed (N/L) n = N / L

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A straight, horizontal wire 100 cm long carries a current of 12 A is at angle 45o to the direction of the horizontal magnetic

• field. Find the magnitude of the magnetic

field, given force on the wire is 500 mN.

EXAMPLE 5

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A) Calculate magnetic field for 10 loops wire with radius of 0.5 m and carries 3 A current. B) The magnetic field at d distance from a long wire is 4 uT, the wire carries a current

• f 6.0 A. Find magnitude of d.

EXAMPLE 6

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Atomic electrons have a property called “spin” that gives them a small magnetic moment. In multielectron atoms, the electrons are usually paired with an electron of the

• pposite spin, leaving no net magnetic

moment. However, this is not always the case, and some atoms do have a permanent magnetic

• moment. They will experience a torque in a

magnetic field, and will tend to align with it.

MAGNETIC MATERIALS

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In ferromagnetic materials, the forces between neighboring atoms are strong enough that they tend to align in clusters called domains. These domains are macroscopic in size.

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When a ferromagnet is placed in a magnetic field, the domains tend to align with it.

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When the external magnetic field is removed, the domains tend to stay aligned, creating a permanent magnet. The most common ferromagnetic materials are iron, nickel, and cobalt. Some rare earth alloys are also ferromagnetic.

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Electromagnets and Magnetic Permeability

Ferromagnetic materials can be used to form

• electromagnets. Putting this material within a

solenoid greatly enhances the magnetic field: Here, κm is the magnetic permeability of the material; for ferromagnets, κm is typically several thousand.

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For commercially useful ferromagnets, a type

• f iron is used that does not retain its

magnetization when the current is turned off

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A “permanent” magnet can lose its magnetization through impact or heating. Every ferromagnetic material has a Curie temperature, above which the thermal motion immediately destroys any magnetic alignment (called paramagnet). Lava flows “freeze” a record of the Earth’s magnetic field at the point where they cooled below the Curie temperature. In this way, historical values of the Earth’s field may be determined.